If I understand Source correctly, it is specifically a “this session” creature.
For what you want, there is the Playlist, the list of things (whether on Timeline or not) which we want to keep as persistent between sessions on our project.
Thus, the correct procedure would be:
Load source video into Playlist
1a. Load Playlist item to Timeline
Cut a piece at the end
Save project
Notice one can still switch between Source and Project
Exit Shotcut and restart, select the same project
Double-click on item in Playlist; it becomes a Source again
The source is transient. It changes whenever you double click a playlist item or timeline clip. It also changes any time you open a new file. It is not intended to be saved when you close and reopen a project.
I understand now. I I think some names like Source and Playlist may be hard for beginner. I have some suggestions but probably I need to use Shotcut bit longer.
For a non-linear editor it is essential to keep a link to the the original videos. As a result those videos should be required to be in Playlist, rather than optional as it is the case right now.
All you need to is from the timeline is copy the clip, and it copies it to the Source player. Also, you view Properties and get the full filename or go to it in the system file manager.