Having updated to iPadOS15, you’ll not be able to restore an earlier version of iPadOS.
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. At present, the only available update for devices capable of running iPadOS15 is the current version - iPadOS 15.2.
If you have an App that is not compatible with the installed version of iPadOS, you will need to seek assistance of the App Developer - as only the Developer will be able to update the affected App:
How to contact an app developer - Apple Support
If data associated with the App is critical, do not uninstall the currently installed App, as doing so will also delete the App’s associated data. The regain access to this data, unless the Developer can offer an alternative, you’ll need to wait for an update before you’ll be able to access the App’s data.