"Do you think it could also solve the problem when I assign a permanent IP Adress to my homepod mini through the router settings?"
No
"Apple Support today and it looked like they had no idea... "
I wouldn't pay too much attention to that.
"I would have my peace if I would know that Apple is working on this and will be able to solve it (an official announcement from apple would be nice...)"
Multiple sources including reliable tech magazines have reported a fix is on the way. "official announcements" are not all that common until a fix is implemented.
I have said this before but it is my experience that Apple fixes all relatively common issues. It would be very uncharacteristic for them not to fix this one since it has been publicly reported in multiple venues.
( I know this issue is annoying but a word of advice, unasked for I realize, which is that one shouldn't lose peace of mind over something as trivial as a HomePod that doesn't answer Siri requests. If you, your family and your loved ones are healthy, that should be enough. My take anyway. Be well.)