So BGA has a thing where if you're over time on a game, you can't actually play any of your other games (or start any other games) until you play that one (it may only be for Arena/tournaments, but it's definitely a thing). I've been annoyingly hit by this where a game finishes on me overnight and I go to kick off a new table of that game before I get into playing my moves and forget to and BGA won't let me. So I wasn't sure how a player could be that far in the red and playing other games - you got me curious about what was going on here.
I looked at your active games, and I couldn't see any 7 Player 7 Wonders games going on.
So I looked at your recent tournaments and found one that has 7 Player games. And the game you're in is about 50% done and the player who's turn it is is 9 days in the red. So I'm pretty sure this is the game you mean.
Except I'm still very confused. Cause ANOTHER player was booted from this game about 10 days ago, everyone has left except one player (including both you and the player whose turn it currently is), and all the moves should be AI(ish - BGA's AI for this sort of thing tends to be pretty rudimentary, I think basically taking the easiest move to keep the game progressing). I don't know why the AI hasn't taken the turn for the player whose turn it is, but it doesn't matter anyway as the game was over as soon as that other player got booted.
Though, I'm not sure what happens if the last person doesn't leave the table. Typically there's two outcomes in tournaments where a game is aborted - booting and max timeout. This is obviously a booting situation, but if the last player doesn't leave, does it become a max timeout scenario? Because that will affect rankings - bootings result in rankings awarded possibly by seniority, possibly entirely randomly, while max timeout goes to whoever has most time remaining. Either way, there's little you can do to affect the outcome here.
But as to why the player 9 days in the red isn't taking their turns? They're not at the table anymore. BGA isn't telling them they have a turn to take (and by rights, they don't). If you want to speed things along, you could message the person who is the last one at the table, and ask if he wants to exit so the tournament can move on, but it might be that he's holding it open to affect a max timeout game end instead of a booting game end. If that's the case, then you've got another 11-ish days to wait.