Thank you! My confusion is lifted. Perhaps I can help others too. I think I've pieced together some Cressi history.
The new Donatello UI makes good sense. The previous answers explain it. Selecting "Gage" mode means a display of depth, time and temp only. So the device is still on. But it is not calculating or logging tissue saturation or showing NDLs. So you could say the computer is off. [I wouldn't, but I guess others might.]
The older Cressi UI was misleading (IMHO). This older UI appeared on older devices and possibly on older versions of Donatello firmware. It is referred to in many, many online reviews of the Donatello. In this old UI, you navigate to the "Gage" mode setting, then hold the button to toggle it "ON" or "OFF". Turning the Gage mode ON was turning the tissue computations OFF. And turning Gage mode OFF was turning them back ON. That's a terrible UI. No wonder they changed it.
Here are some examples from online reviews of the Donatello. They seem to refer to the older UI. These are what confused me. I guess this is all obvious to someone who knows that depth, time and temperature are not "dive functions."
From divein.com:
Ability to switch off all dive functions when swimming or snorkeling.
From deepbluediving.org:
The Donatello has the capability that you can switch the dive computer functionalities off even if you are in the water. The ability to swim and snorkel without dive calculations is a great new feature. You can deactivate the dive computer functionality, which makes it possible to use the watch for any kind of water activity, like snorkeling, without switching decompression calculations on and confusing the dive computer.
From divers-supply.com:
Donatello is an underwater and freediving computer. It is ideal for other water activities, thanks to the deactivation option of the “dive” functions, that avoids unnecessary alarms while snorkeling or swimming.
Also, I asked this same question on Amazon a few days ago. The answer I got from "Cressi 1946 Seller" seems wrong to me. It seems to refer to the older UI that is not on my Donatello:
To be precise it is called the "Gage mode" function, ... . To enable it, you need to navigate the menu until the GAGE item appears. Press and hold the button for a second until OFF flashes, short press to set it to ON, and long press to save. It's very important to enable this function only when swimming and never when scuba diving. It is recommended to reset it to OFF when you stop swimming before any future scuba dive.
Set it to OFF to turn the device ON for scuba. Makes great sense!