How to put iPad to sleep or turn off when it’s always plugged in.

What you're describing here and envisioning here seems quite reminiscent of a Windows system and a screen saver and a CRT display.

iPad is not that, and operates differently from desktop computers around power and cooling.

iPad sleeps when the display is not active, and that whether or not the iPad is connected to power.

This sleeping happens unless some app is active in the background (such as iCloud backups, checking for updates, etc), and that's up to the app developer. And even with background activity among one or more apps, the display is still blanked.

There is no means to do what your partner wants here, so replacing this iPad with Microsoft Windows or an iMac seems the appropriate approach if you want those technical display-handling features. This rather than the tap-to-wake the iPad, as I've suggested enabling above.

(Macs are increasingly operating similarly to iPad here too, and seek to reduce the time that the computer is awake, and to reduce when the display lit. I'd suspect Windows is making progress in this area of power management as well, but haven't checked.)

A heavily-used iPad in a critical role is probably going to end up getting replaced somewhat more often than a home-use iPad, too. This due to the added wear, and due to the need for the iPad—or any other computer in this role—to perform reliably. This replacement, or having a ready spare. (As for your case, I'm aware of various iPad Pro models that routinely see 10 to 14 hours of heavy use each day, day in and day out, display blanking fairly short with tap to wake and with the display active, and with no issues.)

And again, log your feedback with Apple here.

Tap to show the display when it’s blank, and the display then blanks itself after some settable number of minutes, which is about as simple to operate as I can think of here while within the constraints. Try it on most any iPad handy, and see…

Closest available is probably the display auto-lock setting.

Settings > Display & Brightness > Auto-Lock

Combine that with…

Settings > Accessibility > Tap to Wake

Which will blank the display after the pre-set time, and then a tap to the display will wake the iPad.

Not what you want, but can get you fairly close…

And to suggest enhancements to Apple: https://www.apple.com/feedback/

Your iPad will automatically power-on whenever it is connected to an external power source. While it is possible to fully shut-down the iPad manually, automatic shut-down cannot be scheduled.

As such, for Kiosk and PoS (Point of Sale) applications, unless manually shut-down, the iPad will remain powered-on.

To turn off iPad, do one of the following:

• On an iPad with a Home button: Press and hold the top button, then drag the slider.
• On other iPad models: Simultaneously press and hold the top button and either volume button, then drag the slider.
• All models: Go to Settings  > General > Shut Down, then drag the slider.