You're using one product that blocks ads and trackers, but then bypassing that with another product that deliberately provides access to ads and trackers, but via a third party.
I subscribed + configured my router to use NextDNS years ago so ads + trackers are blocked on my IoT devices. More recently, I inherited a MacBook and now an iPhone and naturally enabled their built-in blocking capabilities. I think I assumed two blockers are better than one but now I just leave Apple's IP limiting features off and let NextDNS do its thing but it just feels weird to deliberately turn off a privacy feature.
This is not two ad blockers. One is an ad blocker the other is a tracking blocker. They conflict simply.
If you want both across all apps (not just the Browser) you need a VPN service with included as locking, such as protonVPN, IVPN, Etc. There are a lot.
Yes, they are a DNS ad blocker. iCloud private relay is a tracking blocker, to hide your IP. Both are not compatible in general, unless the "IP tracking blocker" explicitly allows to configure nextDNS as a DNS server, which is not the case of private relay.
I guess nextDNS should list exceptions like private relay, but the list is long and it's confusing. For all intend and purposes I agree with the statement, they block ads on most devices.
They also have help articles specifically for VONs:
What is the point of the latter?