Another bluetooth headset that connects but doesn't show in the audio sinks

Bluetooth headset connects:

Screenshot_20200630_113730
Doesn't show up as an output device, although:

Screenshot_20200630_113923

In the audio config -> advanced properties, the device shows up as off:

Screenshot_20200630_114154

Notice there's no A2DP profile available. Setting it to HSP in the dropdown and pressing ok takes no effect, as reopening the audio config shows the profile as off again.

I've tried the solution proposed here, using these commands:

sudo mkdir -p ~gdm/.config/systemd/user
sudo ln -s /dev/null ~gdm/.config/systemd/user/pulseaudio.socket

No effect.

pavcontrol "Configuration" tab shows A2DP ad unavailable and HSP as available, but setting the headset to HSP profile resets back to off as before:
image

I've added pulseaudio-bluetooth-a2dp-gdm-fixpackage, bluez-alsa-git, pulseaudio-bluetooth, bluez-hid2hcito no effect.

How can I enable A2DP for my headset?

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