Restoring iPad apps with Backup

"Hi, thank you for your response. I actually solved it myself just now. It was apparently an App Store issue. I noticed I also couldn’t download any new apps, and the account page of the App Store app wouldn’t load. A simple restart fixed this."

-------

You are welcome..

App Store Issues:

There nothing on Apple System Status that would be of suspicion (as of this reply), though iCloud Mail was having server syncing issues. So, having restarted your Mac, it probably was fixed by that. If you are using a VPN, then that would look suspicious at times to Apple's servers, and syncing with iCloud devices just may not operate as it should. Lastly, having just installed the most-recent update, I was required to sign in to iCloud, representing the fact that an update can get in the way, and the best route around that is to restart your Mac (but, just for the note, back up your Mac prior to installing any macOS update).

“[…]It also seems I can’t redownload them from the AppStore without having to repurchase them. I’d love to transfer the in-app data over. I’m particularly focused on the app Music Studio by Steinberg, but it would be cool to get my Geometry Dash data as well.[…]”

———-

iPadOS Restrictions:

An iPad 2 can only go so far in iPadOS versions. So, incompatibility is likely the issue here. If you are prompted to repurchase the app, then, it is a different item you are purchasing, or the app license is for one device only. So, contact the Developer, asking if they can provide you with a free upgrade. You’ll find their Contact Us info in the app’s site of the App Store. Done so myself, and being that I own the license, I was granted the install, because I was transferring to a newer device.