I upgraded to jAlbum 20. Launched, pressed Add button to add files, I get the spinning pizza wheel, have to Force Quit. Downgraded to jAlbum 19, same thing. Upgraded to jAlbum 20 again, same same. I have to make an album, so I guess I'll try another OS. But at the moment I certainly can't use jAlbum on Mac OS 10.15.4.
Just fishing.... Launch jAlbum, then, from the menu bar, choose jAlbum, About, go to the System tab, scroll down a bit, and take a look at the entry for my.pictures.path. It should be something like /Users/yourname/Pictures. Does that path exist on your Mac?
Also, just to make sure there isn't something lurking, launch jAlbum, then choose Tools, Open Directories, Config directory. Close jAlbum. Now, in Finder, if there's an ext directory, delete it. Ditto for a tools directory. Now launch jAlbum again, and see if you get a better result.
Good. I've updated to the same OS X version here (actually developing jAlbum on Mac, then testing on Windows and Linux). "Unfortunately" I can't trigger the problem here, but I assume that a recent Apple update has broken something in the interface between Java and OS X (we're delegating the file choosing experience to the OS so you get a "native app" experience). These OS interfacing problems have happened before. See if restarting your Mac, then running jAlbum again helps, if not, rely on drag and drop until we've been able to fix this problem.
/Users/myname/Pictures exists in my.pictures.path, check.
But does /Users/myname/Picturesactually exist on your Mac hard drive? (This is really a weak hunch, but it would help to cross it off the list of possible causes.)
Just as another experiment (not sure what it will tell us, but worth trying), please install my Pluto skin. No need to start a project - just choose Pluto from the list of skins, then go to Pluto > Info Page > General > Image and click the Add button. Does that also fail?