The bluetoothctl scan on allowed me to pair the device, but it never shows up in Steam or other programs and will disconnect after a minute or so. According to this It may be an issue with the current bluez stack, so I’ll keep tinkering. It doesn’t help that “switch” “pro” and “controller” are all independently vague search terms and search engines are getting worse and worse at returning useful information.
Bluez seems to be the culprit. My wife’s computer runs Pop, has ver 5.64 and will pair just fine with my USB Bluetooth adapter and controller. Bazzite has ver 5.77.