I’m not finding this documented anywhere but the hhd source code (GitHub - hhd-dev/hhd: Handheld Daemon, a tool for configuring handheld devices.) and it’s active by default on the hhd web interface (hhd.dev), which Bazzite installs by default.
If you’re like me and tried using that button (“select”, the left upper one on the ROG Ally) as part of a long-held chord, you’ll probably be surprised by three quick vibrations and an immediate, unstoppable reboot via systemctl, with no real trace on how that could possibly happen.
Just giving people something to find when they start looking for answers about this! 
Tried it on my GPD Win 4 and not seeing anything like that happen. Maybe it’s specific to the ROG Ally or your configuration of the device or the default configuration used for it.
edit:
OK, just checked and it actually shows in the hhd settings in their showcase gif there that you can disable it. I don’t see any such configuration option on my type of device, so I suppose it must only be available on certain devices for some reason.
Indeed this setting was implemented for the Legion Go and the Ally and for some reason did not get carried over to other devices. If you release the button while the vibrations happen it will not reboot. You can also disable it from the UI.
It was created to prevent data corruption when steam crashes, which can happen when you hold the power button.
It is on by default. Perhaps this is worth revisiting now that Steam is quite stable. When it was created steam was crashing 3 times per day.
This setting also predates the setting that allows swapping select with the Armory button, which allows doing chords with the select button.