Finally found out how to vanquish the insidious systemd-resolved gremlins in recent Ubuntu-based distros
There's this file "/usr/lib/NetworkManager/conf.d/10-dns-resolved.conf" that you have to shadow with a file of the same name in /etc/NetworkManager/conf.d
So then, in this new file, say you want to use resolvconf again. This is the configuration:
(dpkg-reconfigure resolvconf and then reboot. resolv.conf should be correct again!)
@yakkoj that's why I run Devuan where I can when I am working with Debian-based systems.
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