I think it would be helpful for players to know from the "ongoing games" screen when they've been booted from a game but can still take over from the AI, I imagine it would share the same spot as "unread chat messages", and the label would read "You can take over from your AI" in green or light blue text to distinguish it from the other messages, what do you guys think?

I don't remember seeing a feature like that. If so, it would be a nice addition, though a bit niche. :D