WiFi is poor in the house despite a repeater, what to do?

Nice that things are going satisfactorily for you. However, I can only recommend the access point with LAN.

I tested the 600 AVM as a repeater/mesh on the same floor with the FritzBox; the data rate and even reception were much worse than before without the repeater. The 1200 as an access point in the mesh with LAN, on the other hand, works excellently for the other floor, the handover works without impairment during VOIP calls, as does the guest WLAN. However, I have not tested high data rates; 5GHz is inactive for me.

The Fritz devices among themselves with the Fritzbox should already work as mesh. Presumably, you don’t have to set anything extra there.

That would be all the better