Hi Richard,
I'm thinking this may come down to raster vs vector.
Do the Photoshop files contain actual shape paths, or is it all raster? ArcMap pulls in EMF files as a picture marker (which accepts raster AND vector formats). ArcGIS Pro does not allow EMF as a file type for picture markers, and you need to use the shape marker, as you mention.
If Photoshop is not generating vector data (as you would by default in, say Illustrator), Pro may not be able to "see" your shape in the shape marker symbol. I am not sure why the apply button would not activate though, since one would think Pro would have acknowledged your EMF file, even if it couldn't display the shape.
I am currently using the same EMF files that we used in ArcMap in Pro without a problem and they were generated in Illustrator. Maybe it's worth checking those Photoshop files to see if there are actual paths that show up on the Paths panel?
Also, did your previous files from ArcMap convert those symbols to a picture or shape symbol on import into Pro?