For practical reasons, I don't often use the Project Manager. Transcoding H.264 clips will get the whole thing not the cuts used ... or will simply give an error and stop the process. Among other things.
So the easiest, simplest way for me is to copy the project file itself to a different drive/system. The media is all backed up, so for most purposes simply having the project files saved elsewhere covers me.
Now ... in many circumstances this will not be enough, and one does need to consolidate all media/assets of a project. Which ... can be tricksy.
When you say project file do you simply mean the main Premiere Pro session? I've been backing that up on Google Drive as I try to figure out this issue, but I assumed if I lost my original project and had to load this backup I'd have a nightmare as the program tries to find the clips I used..
If the clips haven't moved, there's no problem. The project file is basically all meta ... it's the data of where everything is, what it is, and what you've done to it. It doesn't actually "include" any assets themselves. Just references and links.
And if you do move the media/assets, as long as you know where it is on your computer, you can re-link.