Otdfbt

Am wondering if any of this is true (Hammett, The Maltese Falcon, p. 150).

"The
archives of the Order from the twelfth century on are still at Malta.
They are not intact, but what is there holds no less than three"—he
held up three fingers—"referenees that can't be to anything else but
this jeweled falcon. In J. Delaville Le Roulx's Les Archives de
l'Ordre de Saint-Jean there is a reference to it—oblique to be sure,
but a reference still. And the unpublished—because unfinished at the
time of his death—supplement to Paoli's Dell' origine ed instituto del
sacro militar ordine has a clear and unmistakable statement of the
facts I am telling you."

"All right," Spade said.

"All right, sir.
Grand Master Villiers de l'Isle d'Adam had this foothigh jeweled bird
made by Turkish slaves in the castle of St. Angelo and sent it to
Charles, who was in Spain. He sent it in a galley commanded by a
French knight named Cormier or Corvere, a member of the Order." His
voice dropped to a whisper again. "It never reached Spain." He smiled
with compressed lips and asked: "You know of Barbarossa, Redbeard,
Khair-ed-Din? No? A famous admiral of buccaneers sailing out of
Algiers then. Well, sir, he took the Knights' galley and he took the
bird. The bird went to Algiers. That's a fact. That's a fact that the
French historian Pierre Dan put in one of his letters from Algiers.

Googling just turns up page after page about movie props.

Clarification: this question asks specifically the details about the falcon, starting with bare existance.

Addition: a book by Pierre Dan, unknown whether it contains the relevant letter.

More:

It is not clear exactly how Hammett got his material. He is not known
to have read French, medieval or otherwise, or Italian. His references
must have been gleaned from a secondary source. I have been unable to
locate a simple narrative of the rental agreement between the
Hospitallers of St. John and Charles V of Spain that Hammett would
have had available to him with all of the detail Gutman provides. I
think there must be one; but what is clear, nonetheless, is that
Hammett was reading widely, carefully and thoughtfully.

While the "Maltese Falcon" itself is fictional the object might have been inspired by a real one - albeit one without the exciting Knights Templar and Pirates(!) backstory. The "Kniphausen Hawk" is a bejeweled drinking vessel dating to at least 1697 and is currently owned by the Duke of Devonshire, being ~15 inches high and literally covered in gemstones it would certainly fit the bill (pun intended!) but it has nothing to do with Malta or Algiers and I've not been able to find any evidence to show that Hammet was aware of the Kniphausen Hawk.

These are facts, historical facts, not schoolbook history, not Mr. Wells's history, but history nevertheless. ...

I believe what this is saying is that the following information isn't written down in any history book anywhere, but (in Hammet's fictional universe) did actually happen.

Its meant to both lay out some background information to the reader, and to clue them in that this is stuff the author made up to make his story interesting, and help drive its plot.

As far as real world information goes, you should translate the quoted sentence above as "These are fictional facts my author made up, that are only valid within the confines of this book."