I don't think there is an option to convert these elements... But I agree, it would have been nicer if they implemented these as "Behaviors" instead of fixed elements. It would be nice to be able to have a Field behave like a Popover button also.
At this point you can't convert and existing button to a popup button. Once you create one you can copy and paste it. Hopefully FileMaker will add that feature soon.
What I have done when I liked a button but wanted the new Popover feature was to create a popover from scratch, give the popover "window" an object name and them move the button on top of the popover button. Change the button script to Go To Object. That way the button can call the Popover. Granted it is a kluge, but it does allow me to repurpose the button.
Interesting trick, but I'm not sure why you wouldn't just use the popover instead of the button. However, I have done a similar thing to cover an action on both FM13 and FM12—a button which navigates to a new layout in a new window in FM12. I replaced this with a popover in FM13, but of course the popover doesn't work in 12. So I designed the popover button to be identical in appearance to the standard button and placed it directly on top of the standard button. the layout looks the same in both versions, but the popover in FM12 is invisible so the button activates, whereas with FM13 the popover activates because the button is hidden below it.