No other info.

From all I could tell, I finished the game. Then I got a report that I left the game. I didn't leave the game. What the hell.

I think I am getting exactly this error. In the list of games it appears as my turn but when I enter the game it appears as my opponent's turn. This makes it impossible to play in other lost cities arena games too, as it says I have to play in the inaccessible game first.

The same. According to list of games it is my turn. Arena rule for turn-based games tells me that it is my turn.
But when I access this table I see it is my opponent's turn.
The last action in game log is my opponent playing a card. Next action should be him picking another card, but I don't see it in the log. And upper banner says that my opponent must pick a card.
Everything looks OK, as if it was still my opponent's turn. But...
But it isn't normal for a player to play a card and not pick a next one. It is like making only half of a move. It can only happen when something interrupts (connection issues, real life callings, etc.) or when player do it on purpose. I don't know what happened, it is turn-based game, slow, and my opponent is currently offline, so for now I wait for his answer.
But if it really happened that my opponent made only half of his move and didn't finish his turn, then BGA should not think that it is my turn.
It looks like after a move made by a player it is first written in some BGA log that player finished their turn and it is now time for the next player to take their turn, and second thing written in some log is the record of the move itself. So if anything goes wrong, with connection or database, it can happen that the first thing is saved and the second is not. And we have a table where next player is set as active player, but cannot move, because there is no record about previous player's last action.
If my guess is correct, you should change, or maybe BGA Admins should change something about the time order of saving players' actions and table status changes, or maybe add a condition to check if all actions were saved before changing table/players status.

boardgamearena.com/table?table=342541161

Hi,

I'm not allowed to make my moves, and then I'm expelled, and my karma goes down as if it's my fault. What an irony! Not fun.

I was getting report that it was the other player's turn (and that they needed to pick a card). The game reported that I timed out.

Table #609487581
Move#82
Same problem: both sides waiting for the other cause the game said it was their turn. Both out of time. Refreshing didn't work.