Shelly BLU H&T devices are not detected in Home Assistant

Hello from Germany!
I am new here and my english is not the best...

I have a few Shelly BLU H&T units in use.
Unfortunately, I had to remove all of them from my Shelly app and reinstall/integrate them.
Note to self: ALWAYS write down the MAC addresses.
Well, you live and learn.

In short: I managed to set up all the Shelly BLU H&T units in the Shelly app, and they are working exactly as they should.

Unfortunately, the pesky things won't show up in Home Assistant (HA).
I’ve already tried various things without success.

What puzzles me is that my other Bluetooth devices were detected perfectly (Shelly Button, Shelly BLU Door/Window, Shelly BLU Motion, etc.).

A quick note on this: I recently migrated HA from a Raspberry Pi to a small home server running Proxmox.
Before the move, all the Bluetooth devices were present in HA
(including the Shelly BLU H&T units).

What am I doing wrong?
Does it make sense for me to completely remove the BThome integration from the Home Assistant and reinstall it?

Greetings from Dorsten, Germany.

Please note: My English is not good!

Is your new bluetooth coordinator on the 'good' list? (Is the hardware on your new computer for bluetooth one of these)
Otherwise a bluetooth proxy might work better for you. (This might be a better way to do bluetooth in your set-up)

Sorry I don´t understand you

I figured it out myself:
Settings / Devices & Services / Shelly
Change the gateways from "Disabled" to "Enabled" under Options there,
and lo and behold: the Shelly BLU H&T devices are detected.
I am using the Shelly BLU Gateway (SNGW-BT01) as the gateways.

That still doesn't explain why all the other BT devices
were detected, though. But never mind!

Greetings from Dorsten