Can't restore iPad from backup (iOS too new?)

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.

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.

An iTunes or iCloud backup can only be restored to a device that has the same or later version of iOS/iPadOS than was used to create the backup. In other words, a backup created by a device with iOS/iPadOS 14.8.1 installed, can be restored to a device with iOS/iPadOS 15.x - but not to a device with an earlier version, such as iOS 12.5.5.

As described, either your backup(s) is (are) somehow corrupted - or your iPad has a problem. Given the current status of your iPad, you might be best advised to perform a factory restore - which will fully erase the iPad and reinstall a fresh copy of the most recent version of iPadOS supported by your iPad. Upon completion of the factory restore, you can again attempt to restore your backup:

Restore your iPhone, iPad or iPod to factory settings – Apple Support

Restore your iPhone, iPad or iPod touch from a backup – Apple Support

Restore all content to iPad from a backup - Apple Support

You’ll need access to either a PC (with iTunes installed) or a Mac (with iTunes or Finder - as appropriate for the installed version of MacOS).

Download and use iTunes for Windows – Apple Support

Update to the latest version of iTunes – Apple Support

Use of a PC or Mac computer is unavoidable. If you don’t have access to a suitable computer of your own, that of a helpful friend or family member will suffice. Alternatively, the technicians at the Genius Bar of your local Apple Store or Apple Authorised Service Provider (AASP) will be delighted to assist.

If you continue to experience difficulties, you might be best advised to seek assistance directly from from Apple Support. You can contact the Support Team using the Get Support link at top-right of this page.

Alternatively, if you have access to another Apple device, you can initiate and manage your support cases using the excellent Apple Support App. If not already installed, the App can be downloaded from the App Store:

https://apps.apple.com/gb/app/apple-support/id1130498044

You might also visit the Genius Bar at your local Apple Store or Apple Authorised Service Provider (AASP) - where the technicians will be able to test and assess your iPad:

Genius Bar Reservation and Apple Support Options - Apple

A backup can only be verified as being a “good backup” if it can be successfully restored. If all the backups are common to your Mac, then perhaps the Mac itself is the source of the problem. You won’t be the first, and certainly not the last, to discover that all your backups are useless.

In computing, best practice suggests that for critical data you should have three backups, using two different backup methods - and one should be kept in a separate location.

You might be best advised to take both your mac and iPad along to your local Apple Store or AASP - where the technicians will be able to assess and advise.

Unless you have access to a viable backup of your iPad, other than exploring the possibility that your Mac itself has a problem, it follows that you have [at least temporarily] reached the end of the road…