Transfer iOS app user data from old to new iPad
Browsing this community and other internet sources I could still not find a definite answer to the following problem: I have several apps with user data (example: field guides with my notes, observations, etc.) While some app developers often provide means to export those user data it is some times not possible to re-import them after switching to a new iPad. Is there a method to copy an app "bit by bit" from the old IOS device directly to a new one (similar to "Carbon Copy Cloner on Macs") and if yes which app can do this reliably or is there another way to transfer not only the app but all the user generated data within this app to a new device?
I have the following systems available: desktop Mac Pro: newest Catalina macOS (10.15.7, but I could upgrade to Big Sur if that would help with the problem), old and new iPad both with newest iOS (14.4)
Thanks a lot for any hint!