Home Assistant Green + ZBT-2 do not connect to Thread devices

I wanted to move my devices from Google Home to HASS today.
Unfortunately, it’s not working for any of the devices. I tried an IKEA button (after resetting it) and Eve Energy (also after resetting it).
The devices are detected, but the assistant keeps trying to connect to the old network.
I also deleted the data from Google Play Services on my phone, since login credentials might be stored there as well.

HASS is currently up and running; Thread, Matter, and ZBT-2 are set up. HASS also serves as the gateway router.
I’m stuck. This makes HASS Green useless.

I have a temporary solution. My pixel has the old thread border router permanently stored and I haven't found a way to change it. Resetting the play services didn't help either.

Procedure:
(1) Use a different Android smartphone (with a different account)
(2) Install HASS app
(3) Settings -> Companion App -> Problem Solving -> Synchronize Thread Access Data
(4) reset device to be installed
(5) Add device
(6) Done

I think you have to deinstall (and later reinstall ?) the Google Home App completely and then delete App Data and Cache from Google Play Services. I would also uncheck the option to save the Thread credentials in the Google Cloud:
It's somewhere hidden under Android/Settings/Google Services/Thread Networks , or similar ...

Directly after that, you should synchronise the HA Thread credentials in the companion app.