There is another thread re systemd-resolved and adguard.
Ed Greshko had a solution to use /etc/resolve.conf instead of the stub file
systemd-resolved uses.
"To revert to the previous behavior you need to remove the symbolic link
lrwxrwxrwx. 1 root root 39 Sep 1 17:52 resolv.conf ->
../run/systemd/resolve/stub-resolv.conf
disable or mask systemd-resolved.service, create an empty /etc/resolv.conf and
reboot."
Would that work in this case?