The way DNS is configured in Ubuntu has become overly complicated in the last few versions. Instead
of configuring /etc/network/interfaces, it is now configured using Netplan. But sometimes that
doesn’t even work because DNS is ultimately controlled by systemd-resolv. systemd-resolv
generates /etc/resolv.conf and the default stub DNS uses a local resolver to resolve DNS
hostnames. For some reason, after upgrading to Ubuntu 20.04 from 18.04, the local resolver was not
started or installed. To fix this, you can’t just edit /etc/resolv.conf, you must add your custom
DNS servers in /etc/resolvconf/resolv.conf.d/head shown in the image below.
Restart the system and your custom DNS servers should stick.