The most recent version of iPadOS for the iPad Air2 is iPadOS 15.7.3. The Air2 does not support iPadOS 16.x.
Information about locking/unlocking Notes can be found here:
How to lock or unlock notes on your iPhone or iPad - Apple Support
If you continue to experience difficulties, you may need to seek assistance directly from from Apple Support. 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