CAD I assume that the major app stores, such as the Apple Store and Google Play Store, check the apps of banks as publishers before users can download them.
There are checks in place to ensure the app is genuine. This is true for any app hosted on the Play Store.
CAD But how is the authenticity (integrity) of the apps from the mirrored PlayStore technically ensured? Or is it the real/authentic Google PlayStore?
It's the real/authentic Play Store.
CAD Does it make more sense to obtain sensitive apps via a sandboxed Play Store or via store alternatives such as AuroraStore?
If security is your top concern, you should use Sandboxed Google Play and avoid using the Aurora store.
CAD Side question: How useful is TAN generation and banking on separate sandboxes within Graphene?
There's only one sandbox. You seem to be confusing the purpose of profiles with sandboxing. They achieve different goals.
CAD Does this result in a security-related advantage or is it just more cumbersome?
Probably more cumbersome for your use case.