Steam Controller does not respect Steam controller timeout setting if the Steam Deck was powered on by it

[JDLKMR]

Your system information

• Device: Steam Deck 1TB OLED
• Steam client version 1785799196
• Distribution: SteamOS 3.8.16
• Opted into Steam client beta?: No
• Have you checked for system updates?: Yes
• GPU: AMD (Steam Deck APU)
• Dock Firmware: 0.13.15.133

Please describe your issue in as much detail as possible:

Powering the Steam Deck on using the Steam Controller (via Puck) results in the controller not adopting the currently configured setting in Steam for how long it takes for the controller to timeout after idling. This results in the Steam Controller powering off after a short time, even if the setting is set to, for example, "Never". If the controller is powered on and connected with the Steam Deck already on (including after experiencing this issue), then the Steam setting applies as normal and the controller reflects it from that point forward.

I am guessing that the controller powering the Steam Deck on results in the controller instead defaulting to a built-in firmware timeout period due to the Deck not being awake soon enough to provide the controller the Steam-determined setting.

Steps for reproducing this issue:

1. Power on the Steam Deck using the Steam Controller.
2. Leave the controller idle with the system turned on.
3. Observe that the controller turns off after 15-30 minutes (and not as a result of battery loss), regardless of what the controller timeout setting is set to in the settings.
4. Observe that from that point forward, turning the controller on and connecting it to the already running Steam Deck results in correct behavior, and the issue only stems from the initial boot-up via Steam Controller.