Looking at the logs, I can see that the AX200 looks ok. I’m using an AX201 on TGL, that needs the fw59 too. You are correct the AX200 is standalone, though the AX210 I purchased to test with does not work in my test systems. Locks them up. In my day job we have over 4000 AX200/AX201 windows devices that the 21.x driver is shocking and until 22.30/40 pretty poor. 22.20 was ok ish. I would like to see you running the LE10b2 code (kernel 5.10.30) which has had a number of little fixes both settings app / kernel ...
Regarding 5.1 kernel - 202085 – iwlwifi: 9560: ASSERT 2B80 unsure on the state of that kernel / this bug / that firmware.
We need to check the revision of the BT firmware in the firmware file ibt-20-1-3 - linux-firmware: Update firmware file for Intel Bluetooth AX200 · pop-os/linux-firmware@9e96e50 · GitHub
nuc11:/usr/lib/kernel-overlays/base/lib/firmware/intel # ls -la ibt-20-1-3.*
-rw-rw-r-- 1 root root 9 Apr 17 00:13 ibt-20-1-3.ddc
-rw-rw-r-- 1 root root 773896 Apr 17 00:13 ibt-20-1-3.sfi
nuc11:/usr/lib/kernel-overlays/base/lib/firmware/intel # md5sum ibt-20-1-3.*
ad54af0edef90047fd14d01517f3c8db ibt-20-1-3.ddc
3d65048d633b0960615976852355280e ibt-20-1-3.sfi
That being all the low level stuff. Within the LE10 settings app. What is Bluetooth doing/showing in terms of devices?