How can I get the microphone to work for my WH-1000XM3

I have a WH-1000XM3, and am not sure how to get it's microphone to work. I switched from PulseAudio to PipeWire for this, but no luck so far.

Correct me if I'm wrong, but I believe in order to do this I need to switch to the "HSP/HFP" profile. For the previous version of PipeWire yesterday (0.3.19), when I run

$ pactl set-card-profile "WH-1000XM3" HSP/HFP

No sound comes out of the headphones anymore.

I was hoping the latest PipeWire (0.3.20) supported HSP/HFP on the headset finally, but now it doesn't appear at all. When running pactl list cards I get:

Card #44
    Name: bluez_card.CC:98:8B:A8:5E:10
    Driver: bluez5
    Owner Module: n/a
    Properties:
        device.api = "bluez5"
        media.class = "Audio/Device"
        device.name = "bluez_card.CC:98:8B:A8:5E:10"
        device.description = "WH-1000XM3"
        device.alias = "WH-1000XM3"
        device.icon_name = "audio-card"
        device.form_factor = "headset"
        api.bluez5.path = "/org/bluez/hci0/dev_CC_98_8B_A8_5E_10"
        api.bluez5.address = "CC:98:8B:A8:5E:10"
        api.bluez5.device = ""
        api.bluez5.class = "0x240404"
        factory.id = "14"
        client.id = "30"
        object.id = "44"
    Profiles:
        off: Off (sinks: 0, sources: 0, priority: 0, available: yes)
        a2dp-sink: High Fidelity Playback (A2DP Sink) (sinks: 1, sources: 0, priority: 0, available: yes)
    Active Profile: a2dp-sink
    Ports:
        headset-input: Headset (type: Headset, priority: 0, latency offset: 0 usec, not available)
            Properties:
                port.type = "headset"
        headset-output: Headset (type: Headset, priority: 0, latency offset: 0 usec, available)
            Properties:
                port.type = "headset"
            Part of profile(s): a2dp-sink