iPad asking for permission to paste each time I issue the paste command

You mentioned you are running iPadOS 16.1, but 16.2 is the latest version at time of writing. Please update to this software release and then test to see if your problem has been resolved. As a side note, it's always a good idea to run the latest software releases where possible before reporting or attempting to reproduce issues, as an issue you have may have already been resolved in the latest software update.

If you refer to pasting to specific apps then this is by design.

Apps could abuse your clipboard and get access to sensitive private content e.g. passwords.

In iOS 14 this was partially resolved by adding the notification whenever apps reads your clipboard. However this wasn’t a complete solution - nothing prevented the app to read your password just you could notice that process. And those notifications were annoying and ruined the experience.

In iOS 16 Apple brought this to the next level - if the app is optimized to use the safe procedures that clearly make users aware of accessing the clipboard by some command, the app just works without any artifacts (e.g. you can check that in my Speech Central). For poorly written apps you will get constant prompts.

First, I doubt Pages (as mentioned by the original poster) and a yet unnamed e-mail app (most likely Apple Mail) are "unoptimized", especially since Pages is one of Apple's own apps. Second, do you have any evidence or links to documentation (i.e. from the Apple Developer site) you can provide to back up / support the portions of your comment claiming Apple made the changes you mentioned in iOS 14 and 16?

You should find that updating to iPadOS 16.2 will reduce the frequency of these messages, as this behaviour was a bug that Apple has now corrected:

Apple executive confirms incessant iOS 16 clipboard paste permission prompts are a bug

As of iOS 16.2, go to settings and locate the specific app and choose allow, under the paste from other apps.