FritzBoxes are sometimes very **** 
Ask how I know…
One setting that made a lot of problems, was the DNS-Rebind-Schutz (assuming you use german). You can find it under Heimnetz->Netzwerk->Netzwerkeinstellungen->erweiterte Einstellungen->DNS-Rebind-Schutz.
Try setting both, the internal IP address and the local mDNS domain (like .local) for your HA instance.
pi.hole
192.168.178.xxx