As of iOS15 they ask your permission to do this. If you don't your app ads aren't personalized.

But they don't use the same standard permission box that they force 3rd party apps to use.

That's shady....

Because they're Apple and it's their store. Of course they want the box to look fancier :)

Also: There is a HUGE difference (in my opinion) between Apple recommending me other apps based on the ones I already have installed vs Facebook tracking my presence and activity everywhere around the internet.

That’s probably the “personalized recommendations”, and you can switch it off in your profile.

Is it opt in or opt out?

It's there since a few iOS versions ago, but as an opt out. I'm not on 15 yet. From what other people write, I suppose that's changed.

I think I remember having to opt in with a new iOS15 installation.

iOS 15 asks on first launch of app store what you’d like.

What is the message in the opt in/ opt ou5lt screen?

This is the pop-up:

Personalized ads in Apple apps such as the App Store and Apple News help you discover apps, products, and services that are relevant to you. We protect your privacy by using device-generated identifiers and not linking advertising information to your Apple ID. Turning on Personalized Ads increases the relevance of ads shown by letting us use data like account information, app and content purchases, and where available, the types of News stories you read. Apple does not track you or share your personal information with any third parties.

Then a button that says “Turn On” and one that says “Turn Off”.

More or less what I expected. This is basically local device side personalization. You can expect to see this pop up in safari soon. Safari will track your browsing and purchase history locally. At which point all display ads on the web and safari will be served by Apple on iOS.

Opt out, because of course very few people would opt in.

After you explicitly granted them permission.