When launching a GOG game that was added to Steam, then the "game startig" screen shows for a few seconds, and then the screen returns to the game page. The play button is green, i.e. Steam thinks that the game isn't running, but the game eventually starts.
The problem is that both the game and Steam receive controller input at the same time.
So far tested it with Silksong (Linux and Windows versions), and Alters.