Pretty self-explanatory from the title. I think it would be pretty fun to have a server for this.

No. This game is really simple and doesn't have an actual community anyway so there's no point to having one either.

What might make sense would be to join up with some other speedrunning community with the same theme. Maybe "meme games" or "Unity FPS". I haven't found any like that, though I didn't search very hard.