Great work. There might be (more) useful life in my BMT01 
Is there a way to turn these findings into something (easily) digestible by HA?
With some help from Claude, I was able to turn this into an integration that uses my BLE Proxy (gl-s10) to connect to the BMT01 and read the temps.
This is beyond awesome.
The temps update immediately.
The BMT connects to the bluetooth&integration immediately after boot, no 7s button pressing needed.
With the proxy, the range is insane.
Just wow. The BMT just got 10x more useful.
Thank you very much, every in here that made this possible.