Are there any written rules on whether or not component pouches, when purchased, contain components or if users have to find the components and put them in?

If it's automatic, does it auto-fill when you get new spells?

The rules do not specifically say, but all indications are that they "always contain what you need" in them.

Here's what we know...

A Component Pouch costs 25gp and...

is a small, watertight leather belt pouch that has compartments to hold all the material components and other special items you need to cast your spells, except for those components that have a specific cost (as indicated in a spell's description).

source

The rules talking about Spell Components treat a Component Pouch and a Spellcasting Focus the same way...

A character can use a component pouch or a spellcasting focus in place of the components specified for a spell. But if a cost is indicated for a component, a character must have that specific component before he or she can cast the spell.

source

This indicates that you only need to worry about possessing zero-cost components if you do not possess a component pouch or spellcasting focus. This may become relevant if, for example, you are kidnapped by the Drow, stripped of all of your possessions, and escape with nothing but the shirt on your back.

Next, while this is not part of the Sage Advice compendium and Crawford-Tweets are no longer considered "Official Rulings" until they make the compendium...he is still useful for clarification...he made the following Tweet.

Q: How do you handle components that don't have a cost but can't be stored? E.g. the flame for Heat Metal.

A: If you're using a spellcasting focus or a component pouch, free components are abstracted away.

source

While that was not a directly related Question and Answer...the idea that "free components are abstracted away" is pretty clear. You have a component pouch, therefore it is assumed that you have the zero-cost components that you need even when it doesn't make sense for that thing to go in a pouch.

Finally, a touch of logic: a Component Pouch is more expensive than any spellcasting focus (though it does leave your hands free when not actively casting a spell). If, after buying it, you had to run around every single time you leveled on mini-quests to stock up your component pouch--then the pouch is patently inferior to a spellcasting focus. It doesn't really make sense that the rules would treat a Component Pouch as equivalent to a Spellcasting Focus if it, ultimately, is not.

It contains a complete set of commonly required, non-valuable, non-consumed spell components, and doesn't need to be refilled unless something unusual happens to it.

But the full answer will depend mostly on how the component pouch was acquired.

The listed price to purchase a component pouch (PH p25) is 25 gp; compare this with a pouch (5 sp) or a backpack (2 gp). It is quite safe to assume that upon purchasing a component pouch you are also purchasing a complete set of common spell components contained within.

As described under Spell Components (PH p203, emphasis in original):

Casting some spells requires particular objects, specified in parentheses in the component entry. A character can use a component pouch or a spellcasting focus (found in chapter 5) in place of the components specified for a spell. But if a cost is
indicated for a component, a character must have that specific component before he or she can cast the spell.

If a spell states that a material component is consumed by the spell, the caster must provide this component for each casting of the spell.

So, RAW indicates that simply having a component pouch is a suitable substitute for a material component, so long as that component has no cost and is not consumed. The contents of a commercially acquired component pouch do not depend on (and therefor do not change because of) what spells you know. It is a standard set of components that any spellcaster might require.

However, if a component pouch was not purchased from a shop, you may find it is not complete. The pouch itself is not a magic item, after all; it is mundane, and may not have had a completely happy and safe existence thus far.

A DM may also decide that a spell component pouch purchased (or discovered) in one location isn't equipped with the components for an obscure, foreign, forgotten, or novel spell (or school, or collection, etc) depending on the campaign's setting and context, or any narrative/player power reasons they feel are important.

The rules don't say if it comes full or not, but it doesn't matter RAW

Component Pouch. A component pouch is a small, watertight leather belt pouch that has compartments to hold all the material components and other special items you need to cast your spells, except for those components that have a specific cost (as indicated in a spell’s description).

This is all the information the book provides us about the pouch itself. And nothing about it indicates that materials come in it when purchased.

However, the component pouch costs 25gp and weighs 2lbs compared to the other pouch in the adventuring equipment table which costs 5sp and weighs 1lb. Now this is very circumstantial, but that cost technically represents something in-game. It could be it's materials or construction or rarity — or it could be what is inside. (See Are there any practical differences between a belt pouch and component pouch in 5e? for more details on the comparison between the two items).

Regardless, the rules don't say if the component pouch comes full or not so that is up to the DM.

RAW it doesn't matter if it is full or not

A character can use a component pouch or a spellcasting focus (found in chapter 5) in place of the components specified for a spell.

The rules for spellcasting say that you just need a component pouch that can count in place of the components themselves. It doesn't say the pouch actually has to contain the components (or really anything).

The game just uses a pouch as an abstraction by intent

Jeremy Crawford has provided a bit of unofficial clarification on the matter of what the purpose of the component pouch is in a Tweet¹:

If you're using a spellcasting focus or a component pouch, free components are abstracted away.

Basically, the intent is, if you have a component pouch the designers intended to have you never have to think about components that do not have a cost.

Your DM can of course rule differently and make you purchase each ingredient to painstakingly fill the pouch but that kind of verisimilitude isn't fun at many tables.

^{1 - Thanks @guildsbounty for pointing this out in their answer.}