Hello,
There are several related things being discussed here so allow me to summarize them.
1) Backstage was never supposed to have its items supported in the QAT. I checked v19.1 and did see that the menu items of a popup button did incorrectly allow the Add to QAT menu item to filter through on its context menu, but that option wasn't supposed to be there and in more recent versions does not show up.
2) Backstage is set via the Ribbon.ApplicationMenu property, but it's important to know that it is not the same as an ApplicationMenu control, and it has very different capabilities. Backstage overlays the entire window, compared to ApplicationMenu, which is a more classic smaller popup.
3) ApplicationMenu (not Backstage) supports items being added to the QAT in both v19.1 and in today's version. Those are the items you see in the "Application Menu" category in the Customizing the QAT sample. When you add those items to the QAT, click Apply Changes, click Save QAT State, and then click Load QAT State, you see them reappear. But again, per #1, this was not intended to be supported for controls on Backstage. It's only meant for classic ApplicationMenu control items.
4) In your last reply, you mentioned images not showing up in the right-side ListBox for some items from the Application Menu category. That is because the ImageSource property is only copied for controls with ImageSourceSmall defined. A number of the items in that particular sample's Application Menu only have ImageSourceLarge defined and not ImageSourceSmall. If you add an ImageSourceSmall property onto all those, you should see the images.
I hope that clarifies things.