voik
Ahhh, loads of them!
D&D adjacent stuff like Pathfinder 2e.
PBTA and kin like Dungeon World, Monster of the Week, Ironsworn. Blades in the Dark.
Delta Green.
I have a whole folder of freeform, GMless stuff like Microscope, Kingdom, Follow, Archipelago, Dawn of Worlds, Dialect, Intrepid, The Quiet Year.
Gonzo one shot stuff like Paranoia, The Sorcerer Supreme, Ten Candles, peace was never an option (think untitled goose game: the rpg).
I recently had a test run or two of Fate Condensed and got completely hooked.
Most of those I'd be content to run or play, but the game I really want to GM myself is a campaign I've been dreaming up for about year now that I call the "sedition sandbox". The scope is focussed to a single city, the capital of a hostile foreign empire. The PCs are an elite team of saboteurs and infiltrators, sent by a nation desperate to turn the tides of a losing war. Their only objective is to bring down the empire from within. Intrigue, plots, rebellions, sabotage, faction politics, assassinations, propaganda, blackmail, anything the players can think of to achieve that goal is fair game. How far will they go to stop the greater evil?
I think it would be a blast (naturally, I guess), and one or two players in my local network have expressed a little interest, but I've yet to rally the kind of commitment I think I'd need to really get off the ground. And the inexorable march of time makes it less likely with every passing day, as my friends either move away or are subjected to all life's little tyrannies of responsibility ¯\_(ツ)_/¯
Seconded! OP, in a similar vein as the world building games you already mentioned, you might find Intrepid interesting. I could see it being used to do world building + history of some of the major players and nations therein.
I could also imagine the relationship map it uses being hacked a bit to allow for some Disco Elysium style personality skills / thought cabinet shenanigans if you were interested in leaning into that in particular.
I think you've received lots of great advice here already. One additional thing you may want to keep in mind as you're weighing your options is how the manner in which this character exits may impact other players.
Obviously, the needs of this player come first, and making whatever changes they need to ensure they can keep having fun in the game is most important. But I bring it up because, in a similar situation where I was running a game for a player who wanted to switch characters, I executed the change in a bit of a clumsy way that one of my other players found frustrating.
I had worked together with the player who wanted to change to craft a heroic last stand scenario in which their old character would sacrifice himself to allow the rest of the party to escape. Critically, we didn't discuss these intentions with anyone else at the table. One of my other players picked up on what was happening the moment we started playing it out, and did everything he could to prevent the loss of a party member. I essentially railroaded right over anything they tried.
Afterwards, they told me that while they understood why I ran it that way once the other player had a chance to explain their intentions and new character, it still wasn't very much fun to play through in the moment.
All this to say, if I had to do it again, I would make sure I have some sort of buy-in from the other players. They wouldn't need to know all the details, certainly, but I think a little heads-up would have made that experience much smoother for everyone.
Some really interesting ideas here, downloaded!