packoman
As @DeletedUser87 said "Private DNS" probably isn't what you want for lan DNS as it involves setting up a local certificate authority and signed TLS certificates.
If you wish to solve this with a static IP on your phone, you have to fill in the IP and field with an unused IP from the static range on your subnet. And fill in the IP of your gateway (router) if it's not ....1 on the local subnet.
A better approach however, would be to configure your router to advertise your AGH server as DNS server for your lan and leave the phone on DHCP. How this is done depends on your router. The technical name for this option is "DHCP option 6".
Hardcoding your AGH server as DNS in wireguard is a perfectly acceptable solution if you want to be able to resolve local domains or just use your AGH filter lists on your phone when you are out and about. In fact it's what I would recommend for your wire guard config.