NM should put IPv6 DNS servers before IPv4 DNS servers in /etc/resolv.conf
According to RFC 8305 (Happy Eyeballs Version 2), Section 3.1:
In keeping with the Happy Eyeballs approach, queries SHOULD be sent over IPv6 first (note that this is not referring to the sending of AAAA or A queries, but rather the address of the DNS server itself and IP version used to transport DNS messages).
Unfortunately man resolv.conf say that
If there are multiple servers, the resolver library queries them in the order listed.
So I suppose as /etc/resolv.conf can be generated in NetworkManager, it should be sorted as said in RFC (IPv6 DNS servers first). But for me IPv4 nameservers are placed first. Also there is a bag: https://bugs.launchpad.net/ubuntu/+source/network-manager/+bug/936712 which was solved but now it is again broken in my Debian based system. Can you check it in all distributives? I use 1.14.4 version of NetworkManager. To do that ipv6.dns-priority should be set to 1 by default.