Unify the default desktop configs for controllers

[Managor]

Your system information

• Steam client version: 1726256783
• SteamOS version: 3.6.13
• Opted into Steam client beta?: Yes
• Opted into SteamOS beta?: Yes
• Have you checked for updates in Settings > System?: Yes

Please describe your issue in as much detail as possible:

In the May 28th update, there was a note that all default chord configs were unified. https://store.steampowered.com/news/group/4397053/view/4146204937627686654?l=english
The same should be done to the desktop configs (and any other hidden configs that exist like the BPM config). Steam controller for example is missing holding start to switch to gamepad action set.
This was discussed in #10551 (comment)