Concerning Pi-hole, everything is fine in this screenshot. You iPhone is making the query to lb_dns-sd._udp.fritz.box. Pi-hole doesn't know the answer and forwards to to the Fritzbox. This replies with NXDOMAIN and requests Pi-hole should not cache this Blocked (extern, NXRA).
Next time the same query is made, the same happens again.
Concerning Pi-hole, everything seems to work as expected. These queries would also be there without the Pi-hole (and also they'd be replied to the same way by the Fritzbox), Pi-hole just unveils this behavior.
You should contact Apple support about this. In the end you payed a premium price for the device. You would hope this means they have an excellent (technical) service as well that can answer what you can do.