Have you noticed that these ads appear only in the App Store and are not based on invasive tracking across apps and the Internet?

Sure, but it’s got a considerably better privacy model than Google’s ads: https://searchads.apple.com/privacy/ . For a start, you can see what information they used to target you by pressing on the “Ad” button (which is my case is nothing because I’d previously flipped a single toggle switch in settings telling Apple not to use personal data to target ads to me).

Google have a whole website dedicated to that ( what it knows about you), and there are toggles if you want that to be used for ad targeting or shared with third parties.

adssettings.google.com

It’s kind of disingenuous to compare Apple’s search ad feature for just promoting an app inside the App Store, with Google’s Adsense online advertising platform which is multi-platform with video, text, and image ads, even audio at one point in the past, on multiple device types being so ubiquitous it’s almost hard to get away from them.

Search Ads are for the App Store and are completely contextual - eg. you search "translate" and a random translate app shows above Google Translate as an Ad. They don't have ads that target the user, only the search term.

Not to mention iAds. Though apparently they shuttered that a few years ago.