iCloud Private Relay or Proton VPN free or NextDNS/Mullvad DNS

I haven’t tried that myself and I’m not 100% sure, but from my understanding (after reading that part of the paper): yes, as long as it’s configured using a profile or an app.

If a user has configured custom-encrypted DNS settings using a profile or an
app, the DNS server specified will be used instead of ODoH.

An unencrypted DNS server provided by a local network or manually edited
in Settings (iOS) or System Preferences (macOS) will not be used for iCloud
Private Relay traffic.

From the iCloud Private Relay Overview paper by Apple.

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