After having the same problem, I ran several matches and concluded that the stall at the end of a turn is due to a certain card that is still in your hand.
For now, the only card that I have discovered with this effect is the Fireguard Destroyer.
Please look into this more.
Edit: Upon reverting to an earlier update, where this error was not present, the problem persisted.
This suggests that the issue is server-side.
I have begun a list of problematic cards:
1. Fireguard Destroyer
2. Spare parts
3. Clockwork Gnome
4. Rockbiter weapon
5. The coin
One last thing: For some reason, the bot can play the first problematic card if it draws a second.