For example, the banking app I have refuses to be installed from the Play Store on GrapheneOS due to "not-certified" device, but works perfectly fine when installed by Aurora.
The check seems to be purely store-based and never enforced later.
But using Aurora I can install it just fine and it works flawlessly.
(for me, the whole point of using GrapheneOS is privacy and not sending data to Google, so using the PlayStore is not an option)
I'm pretty sure if I try calling my bank or searching the website to confirm the developer's public key fingerprint, there's not going to be any answer. You have to ask Google's servers to give you the APK and trust what it gives you, either via the front-end called Aurora or the front-end called Play Store
https://github.com/privacyguides/verified-apps-android
https://github.com/privacyguides/verified-apps/
I think in general trust is established for Play Store apps by downloading the app with the Play Store on a phone with Google Certified Android. Then the app can get the signing key for storage in the database. Then this can be used to verify APKs downloaded outside the play store.