In my experience all your apps get detected and you can keep updating them via Aurora Store. The first time you'll update each app, you'll be asked to confirm it. From then on Aurora Store can download and update the app by itself after clicking the "update all" button. Please anyone else confirm this, because it's long ago that I made my transfer to Aurora.
In order to set up Aurora to search and install new apps check this out (lately Google rate limits accounts and therefore Aurora can't often search for apps out of the box): https://discuss.grapheneos.org/d/6020-aurora-store-alternative/7
Last but not least: You can look into F-Droid stores (like Droid-ify and Neo Store) or Optanium as alternatives and backup solutions to Aurora Store. Some apps have limited or different functionality depending on the installation source. For example VPN apps from Mullvad or IVPN have ad-blocking or account top-up stripped from their Play Store version since it is against Google's rules. Simple Gallery Pro costs money on Play Store, but has a better image/video editor.
Edit: Typos