They've been running ads in the app store since 2016.
Well, yeah, but that's ads running in an entirely closed ecosystem. I guess in a silly way, you could argue that in-app ads with tracking disabled are less effective, and App Store ads provide another way to get eyes on apps, so it kind of competes, but that's like saying that Special Rollback Deal signs inside an individual Walmart store compete with Google AdSense. It's technically correct, but not particularly interesting.
Put another way, I can't imagine that any significant number of people who, prior to the do-not-track rules, used to think that in-app ads were targeted well enough are suddenly thinking that targeting is bad because of those do-not-track restrictions. In-app ads are all too horribly targeted across the board for such a thing to be plausible. And the increase in the number of people choosing to use their ad dollars for App Store category promotion over in-app advertising because of those tracking rules is probably even smaller, if it is even nonzero.
I'm not saying that no judge could possibly find that such claims have merit, because there's always somebody who doesn't understand things who will rule in your favor if you venue shop hard enough, but I am saying that IMO, the claims have little to no merit, at least on the surface, and that Apple's DNT rules A. are likely required by law for European compliance anyway and B. have a legitimate public interest that massively overshadows any mostly hypothetical and negligibly sized anticompetitive impact.