There are other issues with Aurora Store. Outside of GrapheneOS (on which you can use Storage Scopes to mitigate this issue), it requries invasive storage permissions for no reason, as well as other things.
From Wonderfall’s article on F-droid:
If you don’t have Play services installed, you can use a third-party Play Store client called Aurora Store. Aurora Store has some issues of its own, and some of them overlap in fact with F-Droid. Aurora Store somehow still requires the legacy storage permission, has yet to implement certificate pinning, has been known to sometimes retrieve wrong versions of apps, and distributed account tokens over cleartext HTTP until fairly recently; not that it matters much since tokens were designed to be shared between users, which is already concerning. I’d recommend against using the shared “anonymous” accounts feature: you should make your own throwaway account with minimal information.
Aurora Store has its uses, but there are a lot of improvements that can be made to it that would make it easier to recommend.
On a Stock OS on which Google already has privileged access, I do not see the point in using Aurora Store over Play Store.