How can I set up a shutdown after a period of inactivity?

Your iPad will automatically enter its “sleep” state after a period of activity. In this state, the iPad will, by design, continue background housekeeping activities - such as periodically retrieve email and performing regular backup. It is not designed to be be fully shut-down - unless setting it aside for extended periods of many days.

As such, other than manually do so, there are no built-in mechanisms within iOS/iPadOS to fully shut-down an iPad or iPhone.