External Bluetooth Microphone - iPad
I am in a nearly identical situation as you. I have been manically searching for this answer for the past two days, finding little. But here is what little I've found:

The Bluetooth mic is used during phone calls, facetime, and speech-to-text. It is not used for anything related to recording, as if the software is only ok with using that input if the evidence is destroyed immediately, if no record is kept. Wired headphones that have mics built-in will work for recordings, but for some reason the Bluetooth headsets are treated differently. This is true for my iPad mini and for my Android phone.

The most plausible theory I've heard is that there might be some safety regulation that is responsible. Like the government thinks it would be too easy to eavesdrop on people through their headsets if they didn't make these restrictions. But that is just speculation.

Anyway, I hope I was able to tell you something you didn't already know. I will be anxiously monitoring your post to see if someone who knows more than me shares new information. Good luck!!