As long as you are using a per project folders everything should be in your projects folder.
Look and see.
There should be the CWP icon , the Audio folder and the Mix Recall folder inside.
I transfer a lot between machines.
My method for most songs is- I open a Template or a blank project (same thing) and immediately perform a "Save As".
During this save, I browse to the location I want to save the project, which will be a sub folder of my Data drive, Say, " Original Songs" folder.
I open that, create a new folder,
name it for the new song (project),
open that folder, check the Copy all audio box,
name the new song and save it.
I also put any MIDI files and lyrics in that folder, everything to do with that song is in that folder.
I will then drag and drop this folder to a back up drive to transfer.
This creates a back up file which I will date.
This stay on this drive and can be transferred to any other computer.
If I update the song on the second computer, I then drag and drop it back to the external drive and change the date.
I do not delete any versions until I'm 100% certain this is OK to do.