My button (that works for other items) is a Sonoff SNZB-01 (square version).
My issue is the Application statement does not populate with the two buttons I have. Both of which use the built in "Sonoff Zigbee Button Controller" driver.
You want "capability.pushableButton" if you're looking for the "pushed" event, which any button device should support (the capability you identified is indeed deprecated). Other capabilities will look for held, doubleTapped, and released if you need those specifically, but all of them should implement at least this.
To address the other part of your question, I suppose there's some command overlap with this and "momentary," but I don't know that this capability has really seen any real-world use. My guess is that it's a holdover from trying to copy the original ST model (which none of the above was a part of -- except the deprecated capability) that never really caught on (likely due, in part, to these changes to Hubitat model).