https://askubuntu.com/questions/1447098/bluetooth-hci0-is-not-detected-corretcly
"I know that MEDIATEK MT7922 should be able to handle bluetooth, yet I can not turn it on. I tried everything from reinstalling bluez, btusb, etc...
Just now I dicovered that the system seems to think my bluetooth is Foxconn of USB type, even though MT7922 is PCIe."
not identical as yours, but was a bug, kernel-related. That ^ is 11/22 info.
https://forum.endeavouros.com/t/mediatek-mt7922-bluetooth-not-recognized/39841/15
This ^ is the usual troubleshooting (btctl/sysctl/dmesg/lspci) with some twists. But this ultimately solved it:
"Try shutdown the computer. Unplug the power cord. Press the power button for 30 seconds. Then plug it back in and start it up. Some of these onboard WiFi on motherboards have issues. Have seen it before on certain boards."
--I heard of 'letting the gremlins run out' but that took it to another level. That is also dated 3 weeks ago. Both these threads also reminded me that you never mentioned what 90% of inoperable bluetooth threads always mention: thebluez
package/service.
I'm thinking bug or something insanely easily overlooked but you get the first one far more than the second one..