Is there a legal way to downgrade my iPad iOS?

Apple does not support downgrading the OS. Perhaps you should contact the App developer to encourage him to bring his app up to date...

How to contact an app developer - Apple Support

First, some facts…

The ability to restore an earlier version of iOS/iPadOS is possible in limited circumstances.  To be clear, the procedure requires DFU recovery using functionality that is built-in to iTines and Finder. The process, designed by Apple to recover from unforeseen major issues, is not trivial.

All System Updates are digitally signed by Apple - and can only be installed whilst the digital signatures remain valid. After release of a new iOS/iPadOS version, the immediately preceding version continues to be digitally signed by Apple - however, usually within a few days, Apple will revoke the digital certificate with which the earlier version is signed. After a major update, such as the initial release of iPadOS15, the period that the preceding version is signed my be longer.

Now the bad news…

Apple stopped signing iPadOS 14.8 last week - and also stopped signing iPadOS 15.0 just a few days ago. As such, the opportunity to reinstall the earlier versions has now been lost. Until a further update is released, at time of writing, only iPadOS 15.0.1 is signed and available for reinstallation.

Whilst you are now unable to revert to the earlier version of iPadOS, for your interest and in educating others that may come across the question, iMore have a useful article that describes the procedure of restoring an earlier version. The article refers to a different versions of iOS, but the process is the same.

No there is no legal way. Apple does not support downgrading iOS versions.