Can I downgrade my iPad 9 from iPadOS 17.6.1 to iPadOS 15?

Rolling-back to an earlier version of iOS/iPadOS is not possible.

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.

If Apps no longer work properly following update to a more recent version of the OS, you’ll need to seek assistance from the related App Developer - as only they can resolve issues with their App.

How to contact an app developer - Apple Support

Consider that iOS/iPadOS updates include both functional and essential security updates. Restoring an earlier version of the OS would undermine the security of your device and your personal data. 

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I am ever so slightly annoyed with iPadOS 17.4.1

If you post some of the things that specifically annoy your, we may be able to help you better deal with iPadOS 17. It is working without issue on our iPad 7.