Try putting a script like this in /lib/systemd/system-sleep/. Make sure it is executable.
#!/bin/sh
case $1 in
pre)
bluetoothctl power off
;;
post)
bluetoothctl power on
;;
esac
What I said before, looks like a dead end.
~~Start with "cat /proc/acpi/wakeup" and "lspci". My LCD deck doesn't have the new BT chip with wakeup, but I think it might go like this~~
~~Look at lspci, find the Bluetooth there (Maybe it's just part of the wifi?). Note its PCI address, and find a value in /proc/acpi/wakeup that corresponds to that. Take the name from the first column of /proc/acpi/wakeup, and do something like "echo GPPn | sudo tee /proc/acpi/wakeup" . If this works, then you'll want to (a) make a slightly more permanent version of this per the arch wiki, and (b) remember to undo that when Valve finally gets around to doing a proper control for this.~~
https://wiki.archlinux.org/title/Power_management/Wakeup_triggers
Oop. Look up. I changed the parent post, maybe this time it'll work?