ZeroTier, Tailscale, and several other UDP based mesh protocols will sometimes work in “free” mode on planes, but it tends to be horrifically slow.
And there's already a protocol to proxy over QUIC, called MASQUE.
Some of them will try force you to use their local resolver, but often UDP will be left open (or left open on port 53) because it is easier.
When they force a local resolver you can often tunnel over DNS requests, though this only works sometimes :)