My Air2 is older than your 9.7 Pro and I have no issues like you describe. You may have some corruption in your software or possibly a hardware issue like the battery. iOS 14.4 is releasing today, so you could try to update and see if anything changes... If that doesn't work you might want to try and restore using iTunes (without using your backup) to see if it clears things up. If not you can always restore using your backup and everything will be back to where you're at now.