photos crash

Where is the photo you are trying to add to an album? In "All Photos" or a shared album, or in "Imports"? It is not possible to move a photo to an album, you can only add to an album.

There has been a known bug, that photos would crash, if we tried to add photos from a shared album to a standard album, if one of the photos has already been imported to Photos, but I thought, that this bug has been fixed in Photos 5 on Catalina.

You may encounter unexpected glitches, if you upgraded to Catalina, but did not prepare the Photos Library for the migration by removing all image files and video files, that are in a format, that is no longer supported by the new system. Do you still have photos and videos in a legacy format in your Photos Library, as described here for iMovie? About legacy media in iMovie for macOS - Apple Support

Are you using iCloud Photos? Then I would wait, until you are no longer seeing "Uploading" below the All Photos album. Wait, until Photos has finished to update the library after importing photos.

How are you trying to add to the album? Are you using the menu "Image > Add to <some album name>" or are you dragging the photos to an album in the sidebar? usually, dragging to the album in the sidebar is easier. You cannot drag to a folder, only to an album.