Well when I was reading your OP, Private DNS was most defenitley not mentioned.
And I'm not good with screenshots
Can you advertise the Pi-hole IP several times as a DNS server in the LAN DHCP service settings?
That solved it for below OnePlus:
If Pi-hole is installed bare metal, you can validate with below one:
sudo pihole-FTL dhcp-discover
The upcoming version 6 release does that default OOTB when you activate Pi-hole's own DHCP service:
$ pihole-FTL --config dhcp.multiDNS
true
$ sudo pihole-FTL dhcp-discover
Scanning all your interfaces for DHCP servers
[..]
dns-server: 10.0.0.5
dns-server: 10.0.0.5
dns-server: 10.0.0.5