Ok, so the resolv.conf is being used to put systemd-resolved in the forwarding path, with it listening on 127.0.0.53. That’s how Mint does things, so don’t touch that file.
Your resolved.conf has no DNS servers or fallback DNS servers configured, so it should just use the DNS servers handed out by DHCP. Either your DHCP servers isn’t handing out a DNS server (unlikely, since other machines work), NetworkManager was configured to not use DHCP DNS servers, or you’re hitting some bug causing the same. I suspect you may have configured NetworkManager for this, maybe it was overriding the VPN DNS. Or maybe you accidentally set the NetworkManager DNS backend to dnsmasq, when it should be systemd-resolved in Mint.
You could try uncommenting that FallbackDNS line and adding a couple space separated DNS servers, maybe your router IP. Mine looks like this:
#DNS= FallbackDNS=1.1.1.1 1.0.0.1 #Domains=
That will hopefully allow VPN DNS to work when it’s connected, and fall back to other DNS servers when not. If not, we could try taking a look at NetworkManager configs. It’s been a bit, I use systemd-networkd now, but I could spin up a VM.
I was pleasantly surprised with Evolution the last time I tried to use Gnome, it used to be a buggy, bloated mess. But alas, I can’t manage to use Gnome for more than a release or two. Now I’m looking for a decent Wayland native alternative to Thunderbird, but it just doesn’t exist without DE bloat at this point. Maybe someone will build a modern replacement for Sylpheed/Claws.