I wrote a utility program for Shotcut that might do exactly what you want.
It can archive all of the project files in one zip-like file even if they are scattered in multiple folders and can restore the project files either to their original locations or to a single folder.
I would invite your feedback as I am actively working on improving this tool.
Here is a link to the topic in the Resources section.
You can include feedback in that topic and/or open an issue on the project’s github page.
Thanks.