WTH can't I add bluetooth devices via/through an ESPhome bluetooth proxy

Bluetooth devices that need pairing, but are too far away from the HA instance:

It’s a pain in the ass when my panel oven falls off the bluetooth network, and I have to take it off the wall, and carry it into the room where my HA server is located for repairing.

It would be lovely to be able to add devices through a bluetooth proxy.

Is this maybe an integration-specific limitation? I admittedly only have a couple devices that require an active BT connection, but I’ve only ever interacted/set them up via BT Proxies (with active connection enabled, obviously).

And that happens automatically?

https://www.home-assistant.io/integrations/adax/

Home Assistant uses Bluetooth LE to configure the heaters, this means the machine running Home Assistant needs to have a Bluetooth adapter and the heater needs to be in range during setup.