Bluetooth microphone not detected

[mjc]

I'm on Manjaro and I recently got a set of bluetooth headphones with inbuilt mic (https://www.amazon.co.uk/gp/product/B07C5VW8D1/).

The bluetooth pairing works fine, and I can get audio output through the headphone speakers, but the microphone doesn't seem to be detected, and the "Recording devices" list on audio settings shows only "Analog Input (Built-in Audio Stereo)".

Any ideas?

Update:

On a cross-post at forum.manjaro.org, a member of the ARM team writes,

I seem to recall something about the wireless chip not being able to do WiFI and Bluetooth (microphone) at the same time. Don’t know if it’s true or not.

And I know we haven’t gotten the microphone part of the headset jack to work (if it’s indeed a dual jack).

Sounds like the problem might not have a solution.

[wrzomar]

I can confirm, that all my bluetooth audio devices on Manjaro ARM have only A2DP profile, which have only stereo output. On default "Debian" (in January, I think) bluetooth audio was barely working, switching to HSP/HFP profile was either crashing bluetooth or disconnecting, restarting bluetooth wasn't working either (only a bluetooth mouse was working back then). Also, my bluetooth speakers worked then in A2DP mode only with single speaker, pairing two speakers together (for stereo output) also was crashing bluetooth. I've kept original eMMC module with "Debian", but I cannot test bluetooth with it, because it was the last thing that stopped working and it was the main reason to ditch "Debian" on PBP.
But on the other hand, it wouldn't be the first time something isn't fully working on Manjaro, e.g. HDMI audio (or whole HDMI in case of mainline kernel), send SMS in KDE Connect, adding projects in BOINC Manager.
Do not let go. You need to test your headset with other distros and something else than PBP, check versions of packages related to bluetooth audio (from firmware to pulseaudio), use ArchLinux Wiki if you're not familiar with bluetooth on Linux.
Do not let go, because the only working microphone on PBP is the left built-in microphone. I don't believe in dual jack on this thing, the microphone in my wired headset was never working on PBP. The bluetooth headsets would be the only solution to recording audio on PBP with something better than the built-in microphone. Try to avoid 2,4GHz WiFi, use 5GHz WiFi or Ethernet to avoid interference.

[wrzomar]

OK, after last Manjaro update 20.10 (maybe, or maybe my headset was just acting weird last time), I have the ability to switch to the HFP/HSP profilie (the second time I've connected to the headset this profile was availaible in bluetoothctl info, in pactl list outputs and in the sound settings). I can hear that microphone is working, but I cannot record anything.