Bluetooth headset won't connect: Bose QuietComfort Series II

[deepfire]

Your system information

• Steam client version: unrelated
• SteamOS version: 2.195
• Opted into Steam client beta?: unrelated
• Opted into SteamOS beta?: Yes
• Have you checked for updates in Settings > System?: Yes

Please describe your issue in as much detail as possible:

The Bose QuietComfort Series II bluetooth headset won't pair properly in SteamOS, using a USB Bluetooth 4.0 dongle, whereas the very same headset&dongle combination pair and work in other recent Linux distributions (f.e. NixOS with bluetoothd from bluez-5.50 and kernel 5.2.11, although it also worked fine on 4.x kernels).

I'm trying both SteamOS's Big Picture UI for bluetooth and blueman-applet.