All iOS apps on the app store need app approval. It’s the same for Googles app store, and I bet Samsungs and Amazon’s as well.
They test your app and make sure it functions and meets some basic guidelines.
The EU isn’t giving 3rd party stores carte blanche to break the rules, so yes apple has to approve it.
I imagine there’s probably some extra rules just for app stores, but if that’s the case (I don’t know) they’d need to be reasonable or they’d get in trouble.
I am curious though if apple can enforce rules on what apps go on the 3rd party store.
Edit: lots of edits for clarity, but also, apple appears to be being a dick in the process of approving this and abusing their position.