I'm not sure I understand the question fully. The
project.qpproj file contains the paths to the images; if you copy the project for someone else, then they will need to use a different
project.qpproj file with the correct paths for them.
But you can have multiple such files in the same directory. So you could have project_yours.qpproj that has all the paths for your images, and project_theirs.qpproj that has all their paths to the same images - both in the same project directory. In the end, the more important stuff is in the 'data' subdirectory of the project, and this is based only on the file name (not the full path). On your computer, you'd just drag project_yours.qpproj on top of QuPath to open the project with your paths, while they drag project_theirs.qpproj onto QuPath on their computer. If the image names are the same, they will work off the same data.
For backups, I tend to select the entire project directory now and then and compress it into a zip file.