Do any of these games have pirate-themed choice and consequences and pirate-themed character progression/talents?
Choices and Consequences? Negro please... although there *might* have been some plot branching in at least one of the Akella games I mentioned earlier, but I'm not sure if there are true C&C,
probably just straight up black and white morality.
Rule number one for Pirate games is keep your expectations modest. The baffling bit is no game ever game close to Sid Meier's Pirates when it comes to delivering the full package.
Granted, the game's systems are very simplistic, but there's no denying it's set a golden standard with everything - finding treasure, wooing ladies, painting the map of the carribean for your favorite action,
revenge plot to drivew the whole thing forward, ship and character upgrade system, etc. There really isn't a game that does it all in one package, which is a shame. A much bigger shame is if you were revisit even the 3D remake,
you'd immediately see how "modern audiences" would reeeeeee at it for being all sorts of "problematic", so I've pretty much given up hope for anyone giving an honest effort making a lookalike.
If I were to be cheeky, I'd say you should at least take a look at this little piece:
https://www.moddb.com/mods/x-piratez
Scraping the bottom of the barrel here, but if we're talking about Oblivionesque role playing (i.e. Larping), I think Assassins Creed Black Flag can facilitate this plenty.
I wouldn't dare call it an RPG, (though you do unlock upgrades so by modern standards...) but it can be an immersive game that's gotten a whole bunch of things right
provided you can ignore another bunch of things it hasn't. And the fact that it's an AC game. It stands apart from the rest of the series in a good way, but the baggage is still there.
In a similar vein, I had high hopes for this thing, but looking at the reviews, it turned out bad in all kinds of ways.
I'm also eyeballing this thing. Not a pirate game per se, but it might be useful for scratching that "this is a ship and you own it" type of feeling which I feel is an important part of this experience.
Not really what you're looking for, but perhaps someone else might find it useful.