Finally there is a fairly easy way to run:

Speech 2 Text -> intents in Home Assistant Text 2 Speech

both running completely local with Rhasspy and PicoTTS, so I don't need to have Google or Amazon listening to everything which we're saying here at home.

Another very cool thing is that with Rhasspy I can change the call word to "Computer" and add the Star ship Enterprise sounds for affirmation, etc.