Issue with bluetooth device

[ericgrand]

Hello!
I'm setting up a new proxmox machine on a GMKTEC nuc M5 plus (Ryzen 7 5825/32 go RAM/1To SSD).
THis is an upgrade from an old HP server, with a restoration of 3 VM and 3 container.
In between, I have set up a Beelink NUC without issue but the device failed after few weeks and was replaced.

The new setup is giving me headaches with bluetooth.
On this NUC, the bluetooth is a MEDIATEK Corp. MT7922 device (combined Wifi and BT).
When doing on the host a lsusb I have the following result:

Bus 004 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub
Bus 003 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub
Bus 002 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub
Bus 001 Device 002: ID 0e8d:0616 MediaTek Inc. Wireless_Device
Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub

Passing the USB Mediatek device to a VM, (Debian up to date), I have the bluetooth option which appear but unable to activate, and doing a lsusb give me the following outpu:

Bus 003 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub
Bus 002 Device 002: ID 0e8d:0616 MediaTek Inc. Wireless_Device
Bus 002 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub
Bus 001 Device 002: ID 0627:0001 Adomax Technology Co., Ltd QEMU Tablet
Bus 001 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub

But hciconfig -a does report a device with no adress...

BD Address: 00:00:00:00:00:00 ACL MTU: 0:0 SCO MTU: 0:0
DOWN
RX bytes:0 acl:0 sco:0 events:0 errors:0
TX bytes:0 acl:0 sco:0 commands:0 errors:0
Features: 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00
Packet type: DM1 DH1 HV1
Link policy:
Link mode: PERIPHERAL ACCEPT

and I'm unable to activate the device...

Running the same command on the host report:

-bash: hciconfig: command not found

Same for the command bluetoothctl...

As per various topic, it seems I should be able to have bluetooth working on the host...
When trying the command service bluetooth start I have the following output in red:

Failed to start bluetooth.service: Unit bluetooth.service not found.

As I'm an absolute beginner in linux, I'm stuck.

Proxmox is last version and fully up to date...

Thanks in advance for your support!