Interesting that it works when the VPN is connected, though. I also believe that systemd-resolved is installed on just about any system using systemd, but often isn’t enabled, without problem. Enabling it would generally involve a resolv.conf symlink and a config, so maybe that config was hijacked by Mullvad (or OP configuring Mullvad), and there’s no upstream DNS server available when the VPN isn’t connected.
I missed that it’s Linux Mint in the original post, and it looks like Mint has started using systemd-resolved. The Arch wiki might be useful to OP on how things are configured:
Agreed, though I don’t think they disabled systemd-resolved, because it still works using 127.0.0.53 when they’re connected to the VPN. So the daemon must be running, unless Mullvad itself has a DNS forwarder using the same loopback. I suspect they either hard coded some upstream DNS server for Mullvad, because Mullvad might not have supported systemd-resolved yet. Or maybe they set a permission on the configs, and something changed with the user context of Mullvad processes.