I did. Tried again just now and it was as simple as you would expect it to be. Worked with right-click Copy. Also worked with ribbon bar Copy and Paste Special buttons. It even brought across attributes in a predictable manner.
Edit: this afternoon I am using cadastral polygons from a different state and it is pasting property parcels with empty geometry... so I'm going to say this is a problem with my data from one state rather than an ArcPro issue. Strange because both datasets appear the same to me. Will update if I can find the source of my issues.