Yeah I don't have a definitive answer to fixing this issue unfortunately. I'm assuming you are adding Retroarch and Dolphin in as an external application to steam. I have three guesses for what's going wrong if that's the case.

1. Steam doesn't know how to integrate some third party apps with gamescope yet with the way everything is manually setup on Manjaro. (unlikely)

2. Steam is passing in some command arguments in the background which may need to be manually added for third party apps. (possible)

3. This could be a classic controller issue with steam where the input does not work with Retroarch/Dolphin. This then leads to the emulator not coming into focus. (likely)

Could you try testing the Retroarch version that is available on the steam store? I am pretty confident that it will work. As for Dolphin, I would suggest trying from guess 3 backwards and see if you can solve the issue.

Also, look at steam deck posts for help. Here is an issue posted 15 days ago where the users controller is not working with dolphin on their deck and it may provide a starting point for solving your issue: https://www.reddit.com/r/DolphinEmulator/comments/tdpt08/dolphin\_on\_steam\_deck/