Add the ability to select between multiple monitors in gaming mode

[BioMyth]

Your system information

• Steam client version: 1719259903
• SteamOS version: 3.5.19
• Opted into Steam client beta?: [Yes/No] No
• Opted into SteamOS beta?: [Yes/No] No
• Have you checked for updates in Settings > System?: [Yes/No] Yes

Please describe your issue in as much detail as possible:

When in the following conditions occur:

• In game mode
• Using the official steam deck dock
• With multiple monitors connected

There is no option to select which display I want to play my games on, the system defaults to the monitor connected via hdmi.

As I use the deck in game mode & desktop mode a lot this causes me to have to plug & unplug monitors frequently which can then cause issues with the steam deck & dock requiring reboots or unplugging everything from the dock and plugging it back in to fix.

Steps for reproducing this issue:

1. Setup the steam deck dock with two monitors
2. Connect the steam deck to the dock in game mode
3. Note that the steam deck defaults to a specific monitor for output with no way of changing it

[BioMyth]

This is my first issue so let me know if it needs any changes!