F-Droid does lag behind and has a range of issues, some are being addressed but not before getting personal toward those pointing the shortcomings out.

https://privsec.dev/posts/android/f-droid-security-issues/

As far as seeing apps in Aurora, please note the version number against your current install, usually you'll find it is the same. You also can't in the main install an app with the same app ID from a different source on top of a pre installed app due to signing keys being different. ie you can't install App A from Store A in User 1 then App A from Store B in User 2 unless the AppID is different.

Use NewPipes in built update method or add their release page URL from GitHub to Obtainium and reduce dependency on F-Droid/Aurora as much as you can. Add any F-Droid apps to Obtainium too to reduce the need to more appstores and Aurora for anything else. Ideally your aurora apps could do with being put in another user alongside our sandboxed Play Services and your own salted and unidentifiable account for the Play Store seeing that is all Aurora provides which also works with unattended app updates that Aurora doesn't.