Just now, i upgraded the firmware to FRITZ!OS-Version 07.25 and the DNS is now working on my Raspberry Pi 400.
I cannot yet say, if my problem is solved but it seems like it. I will reply to this mail if the problem will reoccur.
Here is an changelog https://en.avm.de/fritz-lab/fresh-from-development/updates-improvements/
Or here in the German changelog https://avm.de/service/downloads/update-news/download/show/eyJkaXNwbGF5IjoiRlJJVFohQm94IDc1OTAiLCJ1cmwiOiJodHRwOlwvXC9kb3dubG9hZC5hdm0uZGVcL2ZyaXR6Ym94XC9mcml0emJveC03NTkwXC9kZXV0c2NobGFuZFwvZnJpdHoub3NcL2luZm9fZGUudHh0IiwiaGFzaCI6IjNiYmQ1ZTI5YTg4N2NjM2U3ZjRhZTRhOTY4YjE3OTNmYTA2MWU1NzA1Y2NkYjZlYjA2ODM2NWYwNjEzYWMzZjcifQ%3D%3D/*Improved *- Update process more robust for potential DNS problems
*Behoben* IPv6: Im IPv6 Router Advertisement (RA) mit Option 25 (Recursive DNS Server) wurden zum Teil Bits des Feldes "Reserved" gesetzt
[EN] Fixed: IPv6 Router Advertisement (RA) with Option 25 (Recursive DNS Server) got manipulated bits at the field "Reserved"
*Behoben* DNS-Anfragen des Typs "PTR" wurden teilweise nicht korrekt aufgelöst
[EN] Fixed: DNS Querries with Type "PTR" wouldn't get resolved right.Could on of this changes be the cause of my problems, or the problems other people are also getting?