I've now pulled my hair for hours trying to set a permanent DNS server setting to no avail. Google is very much not my friend right now. No matter what I change, 'system-resolve --status' keeps giving the dns addresses given by dhcp.
I've done all of the steps outlined in this blog (which I found using bad words): https://agaric.gitlab.io/raw-notes/notes/2019-10-22-change-what-dns-server-is-used-for-nameserver-lookups-in-ubuntu-18/
In short, I've installed resolvconf, set static ip and dns through netplan, edited dhclient.conf with 'supersede' etc, but still system is using dhcp dns. I don't want to change the dhcp shared dns because I'm doing a test joining an Ubuntu to a Windows domain so I don't want the entire network using that dns. But I just can't understand (or find an explaination) of how the dns resolver works and how to change it.