Interesting. I also run HA in a container and getting it to pick up my Zigbee dongle was so easy I don't even remember how I did it.

I haven't tried BT, but my HA box lives underneath a couch with a big steel pull-out bed so I don't imagine it would work very well anyway.

I haven't done it either. But it should just be a case of passing the device to the container. You might need to disable the host from using it and pass admin rights to the container too.

But it was also quite easy to pass a USB device to the HAOS VM in Proxmox.

The host I run HA on is Ubuntu server. If memory serves me right, the Bluetooth issue was related to apparmor and dbus restrictions on docker