cannot rearrange apps on home screen

This test, now completed, suggests that your iPad itself may have a fault.

You would be best advised to seek assistance directly from from Apple Support - and request a remote diagnostic test. You can contact the Support Team using the Support link at top-right or bottom-left of this page.

Alternatively and perhaps easier, you can initiate and manage your support cases using the excellent Apple Support App. If not already installed on your iPad, 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

Try restoring to factory settings - and initially set-up “as new” without restoring from your backup:

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

After restoring to factory settings, test re-arrangement of your Home Screens:

Use the App Library and Home Screen to organize your iPad apps - Apple Support

If all is well, you can then restore your existing backup to your iPad:

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

If after you have restored you backup the problem returns, you will have demonstrated that the problem lies with your backup - and not the iPad itself.

As such, you’ve not successfully proven that the issue is not with settings saved within your backup.

Perform the reset exactly as suggested - setting the iPad “as new” from the hello screen. Sign-in with your AppleID - but do not restore from your backup.

After performing this bare-bones set-up, test your ability to arrange your Home Screen.

These steps are designed to prove the existence of a hardware problem. Until performed, you’ve proven nothing.

I’m sorry to labour the point, but have you simply reset the iPad from iPad settings - or have you actually restored the iPad to factory settings using a computer?

The factory restore process requires use of a Windows PC (with iTunes for Windows installed) or a Mac computer (using iTunes or Finder - as appropriate for the installed version of macOS)?

Only a factory reset using a computer will fully reset the iPad and install a fresh copy of iPadOS.

Having performed the Factory Restore, did you test the ability to arrange Home Page icons as directed - before restoring from your backup?

No problem at all. We’re just trying to get to the bottom of your issue.

You are very welcome.