SUMMARY
When I connect my headset (Sony WH-1000XM3) it now automatically uses the "Handsfree Head Unit (HFP)" profile and there is no option to pick the "High Fidelity Playback (A2DP Sink)" profile. The only other option is "Off". This was not the case before I updated my laptop (I update everything every ~7 days). Before it always automatically picked the "High Fidelity Playback (A2DP Sink)" profile after connecting my headset. My workaround is forgetting the headset in paired Bluetooth devices, pairing it again, going to "Sound" settings, and switching the profile from "HFP" to "A2DP Sink". But this process is slow and quite irritating.

STEPS TO REPRODUCE
1. Turn on headset
2. Wait for it to auto-connect
3. Go to "Sound" settings
4. Check available profiles

OBSERVED RESULT
1. See and hear that "HFP" was picked
2. Be unable to switch to "A2DP Sink" manually (see "available: no" in "AUDIO INFO AFTER RECONNECTING" below)

EXPECTED RESULT
Use the "A2DP Sink" profile (or the last previously used) after the headset has auto-connected via Bluetooth.

SOFTWARE/OS VERSIONS
Linux/KDE Plasma: 6.0
KDE Plasma Version: 6.1.4
KDE Frameworks Version: 6.5.0
Qt Version: 6.7.2
Kernel: 6.8.0-40-generic (64-bit)
Sony WH-1000XM3 Firmware: 4.5.2 (latest)

ADDITIONAL INFORMATION
Laptop: HP EliteBook 865 G10
Bluetooth: Realtek Semiconductor Co., Ltd. (0bda:c85c)

I also noticed that it now takes ~10 seconds longer to connect whereas before it was almost instantaneous after I turned the headset on. But I'm not sure if this is related somehow.

No configuration was changed. I use my headset daily either for entertainment or for calls, but even then I use a different mic than the one inside my headset. It worked before updates but stopped after updates. Sadly I don't know the exact versions of related packages/libraries/etc.

This happens every time.

I wanted to try an external Bluetooth dongle after I disabled the internal Bluetooth device in UEFI but that has another problem (error br-connection-create-socket right after connecting the headset).

Lastly, I tried my girlfriend's headset (newer Sony WH-1000XM4) and they don't have this problem and work as expected.

AUDIO INFO AFTER PAIRING
Card #3
	Name: bluez_card.XX_XX_XX_XX_XX_XX
	Driver: module-bluez5-device.c
	Owner Module: 25
	Properties:
		device.description = "WH-1000XM3"
		device.string = "XX:XX:XX:XX:XX:XX"
		device.api = "bluez"
		device.class = "sound"
		device.bus = "bluetooth"
		device.form_factor = "headset"
		bluez.path = "/org/bluez/hci0/dev_XX_XX_XX_XX_XX_XX"
		bluez.class = "0x240404"
		bluez.alias = "WH-1000XM3"
		bluetooth.battery = "100%"
		device.icon_name = "audio-headset-bluetooth"
		device.intended_roles = "phone"
		bluetooth.codec = "sbc"
	Profiles:
		a2dp_sink: High Fidelity Playback (A2DP Sink) (sinks: 1, sources: 0, priority: 40, available: yes)
		handsfree_head_unit: Handsfree Head Unit (HFP) (sinks: 1, sources: 1, priority: 30, available: yes)
		off: Off (sinks: 0, sources: 0, priority: 0, available: yes)
	Active Profile: a2dp_sink
	Ports:
		headset-output: Headset (type: Headset, priority: 0, latency offset: 0 usec, availability unknown)
			Part of profile(s): a2dp_sink, handsfree_head_unit
		headset-input: Headset (type: Headset, priority: 0, latency offset: 0 usec, availability unknown)
			Part of profile(s): handsfree_head_unit

AUDIO INFO AFTER RECONNECTING
Card #4
	Name: bluez_card.XX_XX_XX_XX_XX_XX
	Driver: module-bluez5-device.c
	Owner Module: 26
	Properties:
		device.description = "WH-1000XM3"
		device.string = "XX:XX:XX:XX:XX:XX"
		device.api = "bluez"
		device.class = "sound"
		device.bus = "bluetooth"
		device.form_factor = "headset"
		bluez.path = "/org/bluez/hci0/dev_XX_XX_XX_XX_XX_XX"
		bluez.class = "0x240404"
		bluez.alias = "WH-1000XM3"
		bluetooth.battery = "100%"
		device.icon_name = "audio-headset-bluetooth"
		device.intended_roles = "phone"
		bluetooth.codec = "mSBC"
	Profiles:
		a2dp_sink: High Fidelity Playback (A2DP Sink) (sinks: 1, sources: 0, priority: 40, available: no)
		handsfree_head_unit: Handsfree Head Unit (HFP) (sinks: 1, sources: 1, priority: 30, available: yes)
		off: Off (sinks: 0, sources: 0, priority: 0, available: yes)
	Active Profile: handsfree_head_unit
	Ports:
		headset-output: Headset (type: Headset, priority: 0, latency offset: 0 usec, availability unknown)
			Part of profile(s): a2dp_sink, handsfree_head_unit
		headset-input: Headset (type: Headset, priority: 0, latency offset: 0 usec, availability unknown)
			Part of profile(s): handsfree_head_unit