Super interesting development. I have bluetooth working perfectly on latest arch linux 5.13.7 kernel.
Using the other advice here, I downgraded my kernel to 5.12.15 and got wifi and bluetooth working. I then paired a razer naga wireless mouse and Sony bluetooth headphones and used them both just fine for a few days.
Today, I did a full arch upgrade and reboot. This included kernel 5.13.7. This kernel was not working with bluetooth previously. Now, having had paired and used two bluetooth devices on the older kernel and upgrading to the new kernel, my bluetooth devices connected instantly and work just fine.
TLDR; Downgrade to old kernel (like 5.12.15) where both wifi and bluetooth work, pair some devices, upgrade back to latest kernel and bluetooth now works.