I have a Fritzbox 6670 Cable (provider T-Magenta / austrian Telecom), and a HomeAssistantGreen.
I followed the AdGuard setup, went into fritzbox to the local IPv4 and IPv6 DNS and set the local DNS servers to the IP of HA. And in AdGuard i did setup the blockedlists & Sites.
if you do nslookup google.com from a terminal on the pc, what is the output? Should be similar to this, the first ip address should be your ad guard ip.
Is not using the man-in-the-middle DNS address that that software provides. You have to give up control of where you look for addresses so that the adguard can decide for you what is safe.
I think it just too some days. Now out of a sudden it startet blocking! I also checked what you send @The-May the ethernet connection shows the DNS from HA