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I don't have a pi4, but I do have the image, which I mounted to take a look around. I'm more of a Slackware Linux person, but I think I muddled through the process of getting dns stuff.
I'm more of a Slackware Linux person...but here goes.
open the file
with your favorite editor.
uncomment the DNS= line and after the = sign, add your DNS servers. If you have more than one DNS server entry, separate them with spaces.
See if that helps. No guarantees. I'm not familiar with systemd (yet). :-)