Immersive Sims:

Immersive sims are, put very simply, about halfway between a standard FPS and an RPG. They feature player choices and leveling/gear mechanics, but not to the degree of a full role-playing game.

Deus Ex (2000): A masterpiece. One of the greatest games ever made. It's a plot-heavy cyberpunk conspiracy thriller with tons of political elements to it. Leftists will find tons to love about the story and the world. The game makes heavy criticism of capitalism, the military-industrial complex, and government control. Can be a little cringe on depicting China, but is otherwise incredibly on-point about many subjects. In fact, the game has (inadvertently or otherwise) predicted events such as 9/11 and global pandemics with scary accuracy. Play unmodded or with light fixes only - plenty of mods for Deus Ex change the experience completely. The game plays very well, but be prepared for standard old-school gaming jank sometimes. The sequels, Human Revolution (2011) and Mankind Divided (2016) are also great, but not as perfect as Deus Ex. Play those next if your PC can handle them (Human Revolution runs pretty well, but Mankind Divided has no chance on an older PC).

System Shock 2 (1999): Another classic, very much like Deus Ex. Trades the political conspiracy plot for a spooky science fiction spaceship disaster. This game practically invented the immersive sim genre as we know it today. The gameplay is very much like Deus Ex, but can be very challenging at times if you're not careful. I have not finished it yet, but what I have played of it is great. It's not exactly a horror game, but can be scary nonetheless.

Bioshock (2007): Also a "Shock" game made by the same people behind System Shock 2. The plot follows the madness involved after a disaster at a city located deep below the ocean. The story is mostly told through phone calls and audio logs. Bioshock's gunplay surprisingly holds up very well, and the combat is a ton of fun. Like System Shock, it can be a spooky game, but I found it to not really be all that bad. The game also dunks on Ayn Rand indirectly, which is a huge plus.

The Chronicles of Riddick: Escape from Butcher Bay (2004): What? A movie tie-in game? It sounds ridiculous, but this game happens to be a cult classic thanks to its gameplay, which was quite ahead of its time. Follows Vin Diesel's Riddick as he escapes from a supermax prison on an alien planet. Requires no knowledge of the Riddick franchise. More of a stealth game with melee combat, but it has shooting sections if I remember correctly (it's been a while).

Non-shooter Immersive Sims: Putting these here as great story-based First Person games, but they have little to no shooting. Thief 1 and 2 (1998, 2000): Stealth game masterpieces. Games today still do not beat them in terms of pure stealth mechanics. Dark Messiah of Might and Magic (2006): Fantasy action game with a tiny tiny amount of RPG mechanics. Pure fantasy shlock. Very problematic with female character designs. Play this if you love kicking enemies off of cliffs. Dishonored (2012): Another stealth game set in a cool steampunk (technically whalepunk) world. Highly recommend, but it's not a shooter.

Role-playing Games:

Vampire the Masquerade: Bloodlines (2004): Story based game following vampires living in Los Angeles, and the politics and world they live in. Very buggy and broken, but when fixed with mods, it's an incredibly expansive world with lots of role-playing depth. Still jank even with fixes, and combat is passable at best. However, it remains a highly-regarded classic RPG for the stuff it gets right. Has quite a few "seductive vampire" tropes with slightly rapey vibes, like most vampire media.

E.Y.E Divine Cybermancy (2011): Very strange and interesting game that is similar in setting to Warhammer 40k. Setting and characters are incredibly unique. This game is definitely not for everyone. I haven't played it myself, but it's definitely worth a mention.

Fallout New Vegas (2010): I know you've played it already, but I gotta include it simply because no other first person RPGs come close, honestly. Fallout 3 (2008) is similar and lighter on the RPG mechanics, so play that if you get a Fallout urge again.

Final Notes:

These are all just the well-known games. New FPS games come out daily from indie studios, so always check Steam for content or recommendations. Finally, I highly recommend setting up an emulator so that you can play older console games. Setup is very easy these days, and you can find just about every old game at the Vimm's Lair website. If I included great console FPS games, this list would be 40 times longer lol. I'd write a lot more about all of this but I'm running out of energy haha. I hope this is at least a little bit helpful!