Phone connected to BT audio-gateway does not show up correctly in pavucontrol

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

Adapter: 01:00.0 Network controller [0280]: Intel Corporation Wi-Fi 6 AX200 [8086:2723] (rev 1a)

BT device: Pixel 2 XL

Desktop: KDE Plasma 5.22

Distribution: Arch

Versions:

bluez 5.59-2
linux-zen 5.12.12.zen1-1
pipewire 1:0.3.30-2

Description of Problem:

I am using my computer as my mobile phone's audio output through Bluetooth A2DP, but the profile is not correctly exposed in PulseAudio tools.

pavucontrol shows a device with a single profile "Off", and doing anything to this device in the UI breaks audio connection until reconnecting.

pactl shows two profiles: off and audio-gateway, but the latter has 0 sinks and 0 sources, and it seems switching profiles does not have any effect.

How Reproducible:

Always.

Steps to Reproduce:

Connect a mobile phone to computer using Bluetooth, and make sure "Media audio" on the phone is turned on.
Open pavucontrol and switch to the "Configuration" page

Actual Results:

Despite A2DP audio is working, the UI looks like the device is disabled:

Expected Results:

The selection should at least contain the profile current in use.