I've been having weird troubles with MediaTek MT7922 chip on Linux also, where sometimes Bluetooth would just die and will not recover until reboot. After researching the situation with agents, the conclusion seems to be that the firmware is buggy (which is a proprietary blob, so only MediaTek can fix it). There was a workaround - disable low-power/sleep state for this adapter - which helps, but is not great for a laptop (since it increases power drain).

And generally, if you check online, you'll see plenty of reports about problems with MediaTek. I've learned my lesson - just avoid MediaTek in general. Intel adapters seem much less problematic and better supported overall.