Your system information

• Steam client version: 1733265492
• SteamOS version: 3.6.20
• Opted into Steam client beta?: No
• Opted into SteamOS beta?: No
• Have you checked for updates in Settings > System?: Yes

Please describe your issue in as much detail as possible:

Game Recording does not record audio if its playing through a different device. I haven't tested if it doesn't work on wired audio devices via the jack, but what I do know that it doesn't work on Bluetooth devices.
I've noticed this on Deep Rock Galactic (it's the only game i play on the deck nowadays) for now, but I need to test other games.
I have yet to test if it does that in Desktop mode, but I doubt it will break like in Gaming mode, because I use the same bluetooth headphones on my computer, and Steam perfectly records audio from them.
I used the Haylou A35 ANC.
Clip:

https://github.com/user-attachments/assets/64afa833-2aca-4954-af78-670e166c78e2

You can tell that the video didn't pause after I connected the headset: stuff still moved in the background at the usual FPS.

Steps for reproducing this issue:

1. Start (potentially) any game (Preferably Deep Rock Galactic)
2. Connect Bluetooth Headphones (preferably Haylou A35 ANC, but it's probably not the issue)
3. Start game recording
4. Wait a bit (to pad out the recording, preferably there should be sound in the background)
5. Stop game recording
6. Watch game clip
7. No audio