For large player-count non-party-games, counting social deduction as party games, the big thing is to make decisions simultaneously. For years there my go-to game with 7 players was Factory Job. It was published in distorted form as Infiltration, and they didn't support 7 players, I guess to keep components down, although man, why not seize the chance to have a game that works with 7? That's a big thing though, that publishers want to keep components down and that can limit how many players a game supports.
It's fair to say that Factory Job is an Ameritrash-y game; swingy things happen. That's not essential though. Other simultaneous-decision games of mine, aside from not having enough components for more players, often run into an area-of-effect issue. If you play Nefarious with 6, you get hit by too many negative effects from inventions; you can address that with an area-of-effect, but then the game rewards/punishes players based on seating position, which people don't like. This is a result of my approaches to reduce politics. You can have a political simultaneous decision game with 8 players with no problem, e.g. Diplomacy. Or, a more solitaire-y game, where the player interaction is e.g. a race. I played a lot of wordsplay at one point - essentially online Boggle - and there can be 50 people playing and it's fine, someone does the best.
You can have dilemmas that work with a large crowd; it's a different experience but does work. This provides a way to get lots of player interaction into a non-political non-random many-player game without an area-of-effect. I haven't done a large game with such a mechanic though. Factory Job is a dilemma game, but it's small group dilemmas (you aren't so much interacting with people who aren't near you).