You have to use the DNS-over-TLS address for the Android “Private DNS” address. If you try to use the DNS-over-HTTPS address, it won’t accept it as the ‘Save’ button is greyed out.
However, I don’t know whether the Android DNS resolver is using DNS-over-HTTP/3 (DNS-over-QUIC), or just using plain DNS-over-TLS.
Cloudflare have a test page where it’s possible to check whether DNS-over-HTTP/3 (DNS-over-QUIC) is being used (after refreshing). However, this is just testing the web browser, rather than the DNS resolver.
Android so far has only supported DNS over TLS so HTTPS endpoints will not work.
My google play system update is still on 1 June so I can’t test it and Cloudflare, google, quad9 don’t have DNS over QUIC endpoints. If you have already received this update, You can test it by using adguard’s DNS over QUIC endpoints. quic://dns.adguard.com
Apparently two DNS providers (Google and Cloudflare) are hard-coded to use DNS-over-HTTPS. Entering Google or Cloudflare’s servers as the Private DNS provider hostname will make Android automatically add the https:// and /dns-query parts to the URL.
This is unfortunate because it means other servers like the malware-blocking version of Cloudflare’s DNS will continue to use DNS-over-TLS.
The malware-blocking version of Cloudflare’s DNS service is the one all my devices are set to, so it sounds like they will remain using DNS-over-TLS for now.
DNS over HTTP/3 is based on DNS over HTTPS (DoH), but supports the HTTP/3 protocol (I’m actually curious if common DNS resolvers can recognise and use HTTP/3 properly).
DNS over QUIC (DoQ) is based directly on the QUIC protocol and uses the same port 853 as DNS over TLS (DoT) by default, but with UDP.