Well, one possible reason would be you are running PS from the external drive. This also may be why macOS can't find it - it's not installed where it should be: Applications folder on the startup volume. PS may not be installed properly or it has been moved. Another reason may be that PS has opened a document located on the external drive. A third reason may be a file lock on the external drive was not freed once the file was no longer in use.
If you open Activity Monitor, then double-click on the PS process in the list, you will open a panel with three buttons. Click on the Open Files and Ports button. You can scroll through the list to see what files are open. This may help you track down the open file.