Commit 012a68f8 breaks A2DP functionality with unchanged configuration

Dear developer team,

First of all, thanks for your great efforts and your time spent for this project! Unfortunately, I had some minor issue lately, see below.

Bluetooth Radio, Bluetooth Headset, Desktop Environment, Distribution, Version (Bluez, Kernel, and PipeWire):

Bluetooth headset: WH-1000XM3 Linux: 5.11.1-arch1-1 (Arch Linux) Bluez: 5.55-3

Description of Problem: I can't connect to my bluetooth headset, e.g via bluetoothctl connect ...

journalctl says: bluetoothd[775]: src/service.c:btd_service_connect() a2dp-sink profile connect failed for XX:XX:XX:XX:XX:XX: Protocol not available

How Reproducible: Use pipewire with commit 012a68f8 onwards (systemd: add unit files for pipewire-media-session). I bisected the problem. 3a7ce966 works. Maybe I need to change my configuration? I reverted the commit 012a68f8 and it works with systemctl --user restart pipewire-pulse.service pipewire.service.

Actual Results: A2DP Protocol is not available.

Expected Results: Bluetooth audio should work. Pipewire should register its audio capabilities at Bluez.