Can you configure Pi-hole as your router's upstream DNS server (likely a WAN/Internet setting), local DNS server (likely a DHCP setting) or both?
Setting Pi-hole as local DNS server would be the preferred way.
Also, a quick search of these forums here revealed that some Netgear devices' firmware stubbornly refuses to work with custom DNS settings, though the UI clearly allows for it.
Some users got lucky reverting to some older firmware, e.g. Setup on Netgear X4S Router (R7800).
Those latter devices seem to bypass Pi-hole.
As they correctly register with Pi-hole's DHCP, they may be using IPv6 to employ a different DNS server altogether.
Note that DHCP is different from DHCPv6 - IPv6 clients cannot be forced to request DNS servers through Pi-hole's DHCP exclusively.
In fact, IPv6 clients may choose to integrate into your network by a method of their own preference (Stateful vs. Stateless DHCPv6 vs. SLAAC).
To confirm this, try disabling IPv6 on your router.