Ah got, that is a different add-on…
I have the ‘Terminal & SSH’, which is called ‘Home Assistant Add-on SSH server’ as well;
I already read somewhere, that you should not use the ‘official add-on’ for this.
But in the mean time I manged to get a working putty ssh client connection over 22222 with a public an private key.
With some help from another post I manged to mount the disk and edit the config.txt with vi to disable the wifi adapter of the raspberry pi.