There are 2 ways you can save things from PhotoStage: 1- Exporting as a final video in like .AVI or .MP4 or 2- Saving as an editable .SPJ project file.
When you export your slideshow as a video file, you're creating the final product, there's no way to have the editable version back. You can load it back to PhotoStage but as an individual video. This files can be opened with most media players.
When you save your slideshow as a .SPJ file, you're saving the editable version of the slideshow that can be only opened with PhotoStage, a media player can't play this PhotoStage project files. If you don't see your slideshow in the recent projects, look for your .SPJ file at the location where you saved it the first time, as this is done manually you need to remember where it was saved and open it from there.