I have the same issue
Confirming this also happens for me on essentially the same setup (but latest Bazzite and an Xbox controller). It's essentially the only thing that makes me sometimes need a keyboard when playing games on the TV, so although it's a minor bug, a fix would be pretty high impact.
Nothing extracted yet.
Environment
OS: Bazzite (latest stable)
Desktop: KDE Plasma 6.7.1
Session: Wayland
GPU: NVIDIA
Steam Client: Latest Stable
Controller: Sony DualSense (USB)
Reproduction
Expected
The game regains focus and gameplay resumes.
Actual
The game does not regain focus.
Alt+Tab immediately restores the game.
Clicking the game window also restores the game.
Additional findings
Observations:
Disabling KDE's Focus Stealing Prevention allows Steam to come to the front, but does not allow Resume to return to the game.
The game minimizes when Steam gains focus.
Changing the game to Windowed mode does not change the behavior.
Using Wine's virtual desktop does not change the behavior.