I'm working on a project for YouTube (don't ask), and I'm doing a permadeath run for a game. Is it possible to create a permadeath category based on my run?

You need to talk with the specific game's community either through their forums or their discord provided they have one about adding any categories to any game.

Absolutely! If you’ve got a unique idea for a speedrun category, head over to the game’s leaderboard page and use the "Request a Category" option (if available), or contact the game’s moderators directly. Be sure to explain your idea clearly and how it adds value to the speedrun community!