You seem to want to have different games

And that's OK to have different wants and needs, but to play together, you need to be on the same page.

Tools that I have used to get on the same page with my players:

Session 0

You can repeat it any time you want. General description is here: What is a session 0?

You set up a session, but instead of actually playing, you are supposed to talk with your players about the game they want to play, the game you want to DM, and how you can meet in the middle and make it enjoyable for everyone.

Same Page Tool

If you don't know what exactly you should tell and ask during Session 0, you can use Same Page Tool. It is a list of questions you and your players should read together, answer, and discuss. It is not perfect, granted, but it worked well for me in the past.

So what to do in your specific case?

I never been in this specific situation, but I have been in situations when my expectations did not meet expectations of my players.

To me, it seems like the players see this game as a "puzzle" to be solved, rather than a story to experience or a world to explore.

For me, this looks like the exact opposite. Take the gate situation. You have set up a puzzle, one and only way to solve that puzzle, and your players wanted to experience the situation like it was life, with many ways to achieve their goals. Similarly with the darkness - magic users should be able to recognize what spell or magic effect is it. Or at least they should have a chance to try. That's the rules. It was against your puzzle to do so, so you just said no.

So they do want enjoy the story all right. They just refuse to go where you try to railroad them.

From my experience, some level of railroading is needed for DM to prepare, and it is best to tell your players directly that you are not able to prepare for each and every course of action they want to take, sorry, day has only so many hours. On the other hand, I never had players that enjoyed a game with one and only way to solve an issue. If you know exactly what they will be forced do, you don't need players anymore, right?

Let me stress this: railroading is not bad, per se. At least some of it is indeed needed for DM to prepare. But leaving enough wiggle room for players is usually needed for them to have fun. And it is a matter of agreement between players and their DM to decide how wide or narrow this railroad will be, what is and isn't acceptable, and how to communicate about it during sessions.

should I just call them and apologize that the session I had prepared was not what they expected

Yes, you should call them. You should also state that their playstyle was not what you expected, and that is OK, it is a misunderstanding. And then you should ask them to meet for session 0 to make sure you can manage your expectations, and it goes both ways.

Or should I (...) write off the time I spent preparing it as a loss?

Definitely not! After session 0 you will need to adjust it, sure, but no need to throw it all out. From what you wrote I guess you will need to prepare for a more open world with less railroading, but you should establish things like that with your players, not with strangers from the Internet like me.

"This is bullshit. You can't just make up stuff as you want."

Actually, you can. You are their Game Master and making stuff up is literally your job. Stuff you make should fit well with the existing game mechanics, and that's something you need to discuss with your players, but you are free to add effects that are not n the books for the sake of the story. Player who said that owes you an apology in my eyes.

Communication skills are crucial for a GM, and this story suggests yours have room for improvement. Let this session be a learning experience, so you can improve for later in the campaign.

1. Improve your out-of-game communication

With so many TTRPGs and many ways of running the same system, playing with strangers can be problematic because everyone approaches the table with different preconceptions and expectations. For example, you expected the session to function like a story, whereas these players expected it to operate like a solvable puzzle.

Before starting the game proper, you need to have a discussion with your players where you try to synchronize these expectations, or at least come to a compromise. Discuss what the GM's role and players' roles should be, such as whether the GM can “make up stuff” or whether the players should not be looking up spells or creature statistics that their characters shouldn't know.

This conversation, often called a Session Zero, can encompass much bigger picture issues such as the game's tone and roleplay expectations. This out-of-game meeting can really help avoid these problems down the line. And if problems do arise, and the GM-player agreement needs adjusting, then hold another such discussion as needed.

2. Improve your in-game communication

The players cannot read your mind. Their understanding of the game world, and the options available to their character, is limited to how you as GM describe the environment and the objects in it. With TTRPGs, players will often assume that if something is in the scene, such as a door or magical darkness, then they should be able to interact with it in some way. Systems like D&D and Pathfinder tend to reinforce playstyles where if the PCs encounter an obstacle, then they can try to overcome it somehow; if that is not the case, then you need to signal that more clearly.

Whenever you present an obstacle that must be resolved a certain way, then you must communicate the rules of the obstacle. For example, if you want the players to find the key to unlock the door, then you must somehow indicate that the door can only be opened with that key.

Never expect the players to take any one path. If you've presented an unclear situation to the players, don't panic; encourage them to ask questions. If they're getting impatient, then a more direct approach may be necessary to keep the game moving. For example, a common tactic is to have a follower NPC who gives advice for when the players are really struggling.

3. Learn and continue

A formal apology may not be necessary, but the players may appreciate acknowledgment that your GM style was not what they expected. Your next step should be to discuss with these players how to move forward, and how you and they should adapt playstyles to be more compatible.

For me, players doing unexpected things is one of the joys of being a GM.

As I've done it longer, I have started to set up difficult situations that I have no idea how to solve, just to watch my players figure out a brilliant strategy I'd never thought of. Or...just as often...watch them turn a very simple task into a raging dumpster fire.

In the case with the gate, something is keeping that thing shut. If it's a specific spell, there are rules surrounding how it works and how it can be disrupted. If it's a magical effect tied to some creature/god/entity, then someone attempting to breach the gate will get that thing's attention. If they hammer away at it for a while, the Big Bad Thing can materialize (or project an image) and mock them for attempting to enter while XXX monster still lives.

Or, if they players think of a particularly clever way to bypass the gate, let them in and then say that the gate was tied to some kind of dimension door and have the monster appear in front of them.

Random example of players being dumb then clever:

An NPC (chieftain of a tribe) knew where a valuable object was located that the party needed. When the party encountered the chief, they assumed he had the object on his person and killed him. In reality, the object was hidden in a secret tunnel dug into a shear cliff face 500ft above the ground. When the party killed the chief, I figured they were screwed and would have to proceed without this important item.

...but the ranger used his bloodhound animal companion to track the chief's path and then the party hired a bunch of villagers to install pitons in the cliff face. They climbed up and got what they needed without the help of the NPC I'd spent 20 minutes making a backstory/side quest for. So it goes!

PS: I just used the same backstory/side quest for an NPC they met 2 session later :D

I know that MikeQ already spelled out the "Improve your in-game communication" fact, but given that your game is about Dark Souls and that I have played (and loved) the computer game, I think I can tailor an answer to your specific game.

So, you have an impassable door. Impassable doors have always existed in roleplaying games, but in D&D specifically they are almost always magic portals of the teleport-to-another-portal kind (where you need the right key to pass through).

This is because any kind of physical item is destroyable in D&D, be it by punching it really hard, blasting a passage open, casting an antimagic field or some other shenanigans. D&D characters are given a complete toolbox for penetrating into places (I've lost count of the times I've heard "can't we just make a hole in the wall?" in my D&D 4e campaign) and even if they weren't, pencil and paper RPGs come with the assumption that characters, given enough time, can do anything that's humanly possible.

I once had a huge impassable door built inside some caves in a volcano that got completely bypassed by a druid casting meld into stone.

But of course this is not how the world of Dark Souls works. The world of Dark Souls has doors that you can only open after completing a quest or finding the right key.

Yeah, I'm talking about the gates at Sen's Fortress and the crest gate in Darkroot Garden.

While the second door is exactly the kind of door where you hear your character say "It won't budge", Sen's gates have bot an NPC telling the players that they need to do something first and a legend about something happening if you ring both bells (and even a cutscene showing that ringing the second bell opens the gates).

This is a good example of the three clues rule (the players shouldn't be able to miss the fact that they are supposed to do something in order to open that door) and a way to tell your players that the door can't be bypassed yet. Have some powerful or resourceful NPC tell them that everything has been tried already, so they won't even think of losing time trying things that won't work, focusing on the quest that will work instead. In other words, provide them direction.

This not only has always worked since the moment I decided to apply it to my adventures, it is very ingrained in the original game. Which also leads me to ask: have your players played the computer/console game? Do they know that the game features impassable doors? It looks like their expectations don't really match the videogame atmosphere.

The existing answers are great, and I wanted to add a slightly different take in addition to those.

My cardinal rule, derived from experience as a GM (especially when I was new, but not only then):

The game should never grind to a halt.

One of the core tasks of a GM is to keep the game moving. Even if it breaks verisimilitude (which I, personally, value very highly in tabletop games), a kludge of a hint is much better than a wasted hour of actual life on something frustrating and unrewarding.

The key to planning this sort of thing well (again, in my personal experience) is to have a failsafe option for when players don't draw the right conclusions. This is something planned such that it can be threaded into the story, and naturally come to the fore if you need it to advance the plot, but it doesn't have to be your preferred solution to the problem and, if players do what they are "supposed" to do, the failsafe never comes up.

It's also true that players shred careful GM plans as a matter of course, so it's also important to be ready to "break the 4th wall" if (and when) one of your failsafes fails.

In this specific example of the gate, there are a variety of ways it could have been handled in both adventure design and also in the moment.

Adventure Planning Stage Ideas:

• The gate could have an obvious mechanism the players aren't ready for yet (like a slot with an
  irregular shape, or a mystical bar across it which actively harms the
  player characters when interacted with and effectively limits their practical
  experimentation)


• The gate could have writing on it (comprehensible on the spot, or
  through some contact the players already have elsewhere). The writing doesn't
  necessarily need to be an explicit solution for the gate, but it is
  an impetus for the players to do something other than hammer at it.
  


• The gate can have some sort of active repellant which prevents the
  players from spending much time there. Environmental hazards,
  monstrous guards, magical effects beyond your players' abilities to
  disregard, and so on. Anything which suggests that players should
  not linger purposelessly can help players actually receive that
  suggestion.


• Touching the gate could provide some kind of psychic or otherwise mystical impression which
  leads the players on to something else (it doesn't need to lead
  directly to the solution for the gate, but should be a step on that
  path).


• On some arbitrary condition which the players just happen to meet, a new clue appears. Perhaps they struggle with the gate into
  the night, but in the moonlight something new is revealed, or it
  becomes easier to interpret magical traces on the door such that the
  players could learn something they might have known previously with a better die
  roll.

On-the-spot Ideas:

• Your players can be reminded of a clue if they seem fixated on the
  wrong objective. Perhaps one of the clues your players did find was
  written down on a folded piece of paper, which falls out of the
  rogue's pocket as they try to climb the gate. You narrating this is
  likely to lead to players checking that paper, perhaps sparking an
  idea that there is something else for them to do.


• A wandering passerby might eventually come past, and can explain to
  the player characters that the gate never opens, despite enormous
  efforts from previous adventurers to do so. The passerby might also
  convey some sort of hint about an something one of those adventurers
  wanted to try, but never returned to actually attempt. You can convey
  that the gate doesn't open in response to direct efforts from
  people very much like the players' characters, and that some other
  action might help.


• You can fudge a roll that a player makes (adjust the difficulty,
  arrange for even a modest failure to deliver plot-advancing
  information despite not being as helpful as it might have been,
  etc.). This was one of the serious issues in your description: a
  plot-critical element should not be hinged on a player's die roll. If
  something needs to happen (like the wizard understanding something
  about the spell), then failure means the players fail out of the
  entire story. That's TPK territory (not in your setting, obviously), but getting to a TPK is probably a lot more fun than staring at an obstinate door.


• Just tell them. I hate doing this, but while I may allow a token
  effort here or there if a task truly cannot be accomplished by the
  players, no matter what the dice say, then I generally don't allow
  rolls. It's not fun having something like that simply stated, but
  doing so is a lot more fun than rolling dice to no purpose. A plain statement can get the point across if your broader world-building and clue-preparing efforts have failed (and it happens to all of us at some point).

A final note:

You asked a good question-- can this campaign be saved? Of course it can! You have an opportunity here to review more of your prepared content, find other situations that might play out like this one, and prepare for them. Everyone starts out new, no one starts out as a perfect GM, and everyone can improve their GM-ing at any point in their GM careers. Fixating on what you may have done "wrong" is not the way to go-- instead, focus on what you can do better next session, so that your players can enjoy the story you've worked so hard to create.