My stupid guess would be that you have a kill switch from your VPN and it might not have anything to do with your DNS. But also, have you rebooted?
Do you use dnscrypt-proxy or systemd-resolved or something else?
Also check your /etc/systemd/resolved.conf
I use ProtonVPN and it sets up a "leak shield" interface when you start it and destroys that when you end it. It keeps traffic from flowing out over the non-vpn internet. The problem is, if the VPN crashes or doesn't shut down gracefully, that interface kills all traffic.
To test if it's something like that, try pinging an outside address, first by name and then by IP. If you can't get either, it's not the DNS messing you up. If you CAN ping the IP but not the name, then it is the DNS messing you up.
In your wiregaurd config (assuming your not using an app) you may have iptables that makes a killswitch when the interface is up.
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