if you get/have AAWireless dongle you can set it to only connect when it also connects to the radio Bluetooth.
If not You can get a toggle switch USB cable to make disconnecting easier.
Have not tried, but Sonoff has a usb switch that you can control remotely and could potentially use Google Home. https://sonoff.tech/product/diy-smart-switches/micro/
Multi head X like this? https://www.duskopijetlovic.com/x11/unix/howto/dotfiles/2021/12/13/xorg-x11-multihead-two-separate-screens.html