Overwritten & Intricate Character Backstory TTRPGs:
- Universalis totally eliminates the distinction between player and game master. You use irl coins to buy authorship over plot elements as you want to write those particular ones, and let the other players deal with the rest. There's a "scenes" mechanic, in case you want to actually play a role, but you shouldn't feel obliged.
- Reign has a single game master, for mostly traditional tabletop roleplaying, but has a whole extra system for statting out political groups that your characters may lead, be part of, or negotiate with. So if a player wants to gain advantage in Reign, they're best served by a backstory that ties them into some such groups, so they can convince the GM that they can call in the right favors...or armies. The "Company" rules are deliberately loosely coupled with the rest of the game's systems, meaning you could bring them into an ongoing D&D campaign unchanged.
- Microscope is GMless like Universalis, but has a more specific framework for gradually filling in the history of the setting. Appropriate as a Session 0 for a more traditional game, like Reign.