I played a Black Market and drew cards, but it was the last action, so I requested an undo to play another card instead. That caused the game to get stuck. We could grant each other undos, but it just remained in the same place with no way to buy or skip the drawn cards. Trying to reconnect to the game led to permanent "connecting to gameserver" for me. Still waiting to see if I can ever play Dominion Online again...
You could try the following.
Use incognito mode, or a different browser to get to log in screen.
Before logging in use "kick and resign".
Then log back in.