I got this issue as well, but found a workaround so wanted to post here for others: I was able to use keyboard to tab through the fields within the overlay browser. Hitting enter as if left-clicking, I was able to get the authenticator email sent, enter my code, and successfully connect to the game.
Hope this helps folks until they can make a real fix for the overlay.
Wish this worked for me. Keyboard inputs even don’t want to work. Using the EA App instead seems to work fine though, so that could be a temporary workaround if you’re using the new Steam Beta client.
