Proxmox: Bluetooth Passthrough/Bridging to EQ3 Thermostat in Home Assistant

I have set up a Home Assistant VM in Proxmox on a Dell Optiplex 7060 Micro with an Intel BE200 Wifi 7/Bluetooth 5.4 M.2 card, including the most recent kernel and HA versions. I own several EQ3 Bluetooth thermostats (CC-RT-BLE-EQ) that used to work fine when I was running Home Assistant OS on my Raspberry Pi 3 with the internal Bluetooth chip. Before adding them to Home Assistant, they must be paired/trusted manually via bluetoothctl on the host shell (under “Other”):

My issue now is as follows: The Bluetooth controller is only available in bluetoothctl in the pve shell when it’s not added to my Home Assistant VM (“No default controller available“), so I removed it from the VM. However, the previous pairing/trusting to the thermostats is not recognized anymore once I add the Wifi/Bluetooth card again as a USB Device in the Hardware tab to be passed through to the Home Assistant VM. The bottom line is that the Bluetooth adapter can either be used in the shell for pairing/trusting the thermostats or passed through to Home Assistant and used there exclusively, but not simultaneously.