Raspberry Pi4 Bluetooth not working (Bookworm not RPi OS)

I have Raspberry 4 with “clean” Debian Bookworm installed (not an RPi OS)
to be more specific:

lsb_release -a
No LSB modules are available.
Distributor ID: Debian
Description:    Debian GNU/Linux 12 (bookworm)
Release:        12
Codename:       bookworm

uname -a
Linux homeassistant 6.1.0-9-arm64 #1 SMP Debian 6.1.27-1 (2023-05-08) aarch64 GNU/Linux

Everything runs well except I can’t get Bluetooth to work. Any suggestions on what can I do?
If I have found correctly it is Cypress CYW43455 chipset which is supported by firmware-brcm80211 package. I can see there is hci0 device, but not working correctly:

#hciconfig -a
hci0:   Type: Primary  Bus: UART
        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:28 acl:0 sco:0 commands:4 errors:0
        Features: 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00
        Packet type: DM1 DH1 HV1
        Link policy:
        Link mode: PERIPHERAL ACCEPT

#hciconfig hci0 up
Can't init device hci0: Connection timed out (110)

#dmesg | grep hci0
[  930.754592] Bluetooth: hci0: command 0xfc18 tx timeout
[  938.978599] Bluetooth: hci0: BCM: failed to write update baudrate (-110)
[  938.985330] Bluetooth: hci0: Failed to set baudrate
[  940.994607] Bluetooth: hci0: command 0x0c03 tx timeout
[  949.218634] Bluetooth: hci0: BCM: Reset failed (-110)

As suggested at this wiki i have tried this one:

wget -O /lib/firmware/brcm/BCM4345C5.hcd https://github.com/armbian/firmware/raw/master/brcm/BCM4345C5.hcd
wget -O /lib/firmware/brcm/BCM4345C0.hcd https://github.com/armbian/firmware/raw/master/BCM4345C0.hcd

From the behavioral point of view no difference. I have tried with both versions provided by the package and from GitHub as mentioned in the wiki.
Perhaps I’m something missing, as there are RPi OS that can work with this internal BT adapter, just need to find out what am I doing wrong :wink:
Any ideas or comments? To be honest I’m not experienced with Linux + Bluetooth :man_shrugging:

What type of HA installation you got? core? supervised? docker?

Check the Requirements for Linux systems regarding bluetooth and pay attention to the ADDITIONAL REQUIREMENTS BY INSTALL METHOD

HA is supervised.
I suppose this is more of a Debian issue than HA because at the OS level I can’t get the Bluetooth adapter to get running.

Ah, okay. Not sure but maybe there was a regression with newer kernel or bluez?