BT headset is disconnected when remotely changing from A2DP to HSP

[Simon Chopin]

Release of Ubuntu: Noble
Package Version: 5.72-0ubuntu1

My headset changed profile from A2DP to HSP as I received a phone call on my phone (the headset can connect to multiple BT devices).
I'd expect the system to adapt to the new profile (add a new source, change the properties of the sink to signal that it's crappy now, etc...), but instead it completely disconnected the headset.

I'd assume this line in the logs is the reason:

mars 05 16:01:44 pug bluetoothd[2644]: src/profile.c:ext_io_disconnected() Unable to get io data for Hands-Free Voice gateway: getpeername: Transport endpoint is not connected (107)

ProblemType: Bug
DistroRelease: Ubuntu 24.04
Package: bluez 5.72-0ubuntu1
ProcVersionSignature: Ubuntu 6.8.0-11.11-generic 6.8.0-rc4
Uname: Linux 6.8.0-11-generic x86_64
NonfreeKernelModules: zfs
ApportVersion: 2.28.0-0ubuntu1
Architecture: amd64
CasperMD5CheckResult: pass
CurrentDesktop: GNOME
Date: Tue Mar 5 16:03:31 2024
InstallationDate: Installed on 2021-07-05 (974 days ago)
InstallationMedia: Ubuntu 21.04 "Hirsute Hippo" - Release amd64 (20210420)
InterestingModules: rfcomm bnep btusb bluetooth
MachineType: Dell Inc. XPS 13 9310
ProcEnviron:
 LANG=fr_FR.UTF-8
 PATH=(custom, no user)
 SHELL=/usr/bin/zsh
 TERM=xterm-256color
 XDG_RUNTIME_DIR=<set>
ProcKernelCmdLine: BOOT_IMAGE=/vmlinuz-6.8.0-11-generic root=UUID=6bfcd06c-aed1-4da7-949a-dffbf9878bda ro quiet splash i915.enable_psr=0 vt.handoff=7
SourcePackage: bluez
UpgradeStatus: Upgraded to noble on 2024-03-05 (0 days ago)
dmi.bios.date: 12/19/2023
dmi.bios.release: 3.20
dmi.bios.vendor: Dell Inc.
dmi.bios.version: 3.20.0
dmi.board.name: 0DXP1F
dmi.board.vendor: Dell Inc.
dmi.board.version: A00
dmi.chassis.type: 10
dmi.chassis.vendor: Dell Inc.
dmi.modalias: dmi:bvnDellInc.:bvr3.20.0:bd12/19/2023:br3.20:svnDellInc.:pnXPS139310:pvr:rvnDellInc.:rn0DXP1F:rvrA00:cvnDellInc.:ct10:cvr:sku0991:
dmi.product.family: XPS
dmi.product.name: XPS 13 9310
dmi.product.sku: 0991
dmi.sys.vendor: Dell Inc.
hciconfig:
 hci0: Type: Primary Bus: USB
  BD Address: 68:54:5A:94:85:F3 ACL MTU: 1021:4 SCO MTU: 96:6
  UP RUNNING PSCAN
  RX bytes:20697414 acl:97 sco:328138 events:3546 errors:0
  TX bytes:21468970 acl:107 sco:327713 commands:3406 errors:0