How often should the iPad be shut off?

Unless you intend to leave your iPad unused and not recharged for many days, there is no benefit or technical reason to fully shut-down your iPad.

From a full charge, if the battery is healthy, most iPads can sustain about 10 days of inactivity before they will automatically shut-down to protect the battery from deep discharge.

Whilst Apple do not, to my knowledge, provide a specific recommendation, my advice would be to consider shut-down if you do not anticipate using/recharging your iPad for 5 days or more.

I aware of a number of iPads that have not turned off in years.

Restarts to clear rotation lock (an old and now seemingly fixed bug), reboots for updates, and a reboot once every few months to clear some other issue or to test some app.

Otherwise… on, or on sleeping.

Do you have a particular situation or concern about shutdown or about restarting?