It was discussed multiple times. It is advised not to use the private DNS when on VPN.
VPN service apps can also provide their own DNS implementation and/or servers, including an alternate implementation of encrypted DNS. Private DNS takes precedence over VPN-provided DNS, since it's just the network-provided DNS.
Apps and web sites can detect the configured DNS servers by generating random subdomains resolved by querying their authoritative DNS server. This can be used as part of fingerprinting users. If you're using a VPN, you should consider using the standard DNS service provided by the VPN service to avoid standing out from other users.
Source - https://grapheneos.org/faq#custom-dns
Marked text in bold - by me.