Normally, DNS names are resolvable. However, if you enable AdGuard and disable it, clients cannot resolve DNS names (including router itself). You need to re-enable AdGuardHome to continue using the internet
What else did you configure on the router?
Can you change the dns to manual then change back to automatic?
Seems some settings having problems. Generally changing the dns server can fix that.
Drop-in gateway mode and OpenVPN client, but I have turned off the OpenVPN client, as it doesn't work (because it cannot resolve DNS names)
I will do that and get back to you