How to enable LDAC on Sony WF-1000-MX4?

I have tried everything, but I cannont get LDAC to work with Sony WF-1000-MX4.

I've added:

sudo add-apt-repository ppa:berglh/pulseaudio-a2dp

I ran update and upgrade and installed:

sudo apt install libldac pulseaudio-modules-bt libavcodec-extra58 libfdk-aac1 bluez pulseaudio blueman

When I run:

pacmd list cards

I get:

     index: 1
        name: <bluez_card.14_3F_A6_A6_80_11>
        driver: <module-bluez5-device.c>
        owner module: 24
        properties:
                device.description = "WF-1000XM4"
                device.string = "14:3F:A6:A6:80:11"
                device.api = "bluez"
                device.class = "sound"
                device.bus = "bluetooth"
                device.form_factor = "headset"
                bluez.path = "/org/bluez/hci0/dev_14_3F_A6_A6_80_11"
                bluez.class = "0x240404"
                bluez.alias = "WF-1000XM4"
                device.icon_name = "audio-headset-bluetooth"
                device.intended_roles = "phone"
        profiles:
                headset_head_unit: Headset Head Unit (HSP/HFP) (priority 30, available: unknown)
                a2dp_sink_sbc: High Fidelity Playback (A2DP Sink: SBC) (priority 40, available: unknown)
                a2dp_sink_aac: High Fidelity Playback (A2DP Sink: AAC) (priority 40, available: unknown)
                a2dp_sink_aptx: High Fidelity Playback (A2DP Sink: aptX) (priority 40, available: no)
                a2dp_sink_aptx_hd: High Fidelity Playback (A2DP Sink: aptX HD) (priority 40, available: no)
                a2dp_sink_ldac: High Fidelity Playback (A2DP Sink: LDAC) (priority 40, available: no)
                off: Off (priority 0, available: yes)
        active profile: <a2dp_sink_aac>
        sinks:
                bluez_sink.14_3F_A6_A6_80_11.a2dp_sink/#1: WF-1000XM4
        sources:
                bluez_sink.14_3F_A6_A6_80_11.a2dp_sink.monitor/#2: Monitor of WF-1000XM4
        ports:
                headset-output: Headset (priority 0, latency offset 0 usec, available: unknown)
                        properties:

                headset-input: Headset (priority 0, latency offset 0 usec, available: unknown)
                        properties:

The "no" at the end of (A2DP Sink: LDAC) (priority 40, available: no) is clear enough, but just to make sure I ran:

pacmd set-card-profile 1 a2dp_sink_ldac

and get :

Failed to set card profile to 'a2dp_sink_ldac'

Does anyone know what else I can try? I've spent an afternoon trying to get it to work.

I also tried Pipewire, but had comparable results.