"I'm wondering how this compares to Apple’s iCloud Private Relay."
Simple answer: Apple doesn't get your info. Mullvad is one of the non-logging VPN providers so unless you're compromised in some other way (like logging into Google, Facebook, etc) then running a make on your is far more difficult than just serving a warrant to Apple.
I don’t believe there’s any way to completely validate any service providers claims - there’s always a bit of trust required
That said, mullvad facilitates fully anonymous signup and payment, if you’re so inclined… so in that regard even if they’re secretly logging, if your OPSEC is up to par then it’s fairly moot.
Simple answer: Apple doesn't get your info. Mullvad is one of the non-logging VPN providers so unless you're compromised in some other way (like logging into Google, Facebook, etc) then running a make on your is far more difficult than just serving a warrant to Apple.