That's introductory course to systemd's shenanigans. People are going to tell you that you're not doing it properly, that there's of course this setting (unless that other setting takes precedence etc.), yada, yada, yada.
If I really have to suffer systemd the first thing I do is manually edit /etc/resolv.conf and then chattr +i /etc/resolv.conf.
And of course remove/purge systemd-resolved.
Not only is it "always the DNS" but then things turn from bad to worse when "it's the DNS, but with systemd".
Removing systemd-resolved is the first step. The second one is moving to an OS or a Linux distro that doesn't have systemd at all.