Ironically, despite the name used, that YAML isn’t actually acting as a BT Proxy (it doesn’t include the BT Proxy component). It’s directly connecting to the device and handling the data locally rather than just proxying the data to HA. Unless there’s a HA integration, a stock Shelly won’t be able to make that work.
I tried setting a Shelly up as a BT Proxy ESPHome, but never had any luck and never found anyone else who did (it failed with one of the BT components required). No idea if it could handle the YAML you posted.