I tried Tech Support and they told me to post here as it seems to be a bug: Can't connect on PTR only
My PTR client gets stuck at “connecting” or “connecting to the game server” message and doesn’t get through to the main menu. This doesn’t happen on the live client and it didn’t happen in any previous PTR patch. I tried connecting for hours and hours, and haven’t got through even once.
Since my connection to Battlenet and Overwatch live servers is fine, I wonder if it’s a bug on PTR? Is it something else?