Exactly. It's no problem moving a project to another computer if you have both the CWP and the audio folder in there.
But that project will default to what every interface set up you used on the original.
All is good if they are similar in/ outs but often all your in/outs can be changed.
Example I can switch between my Tascam and Scarlett no problem, But old projects I composed using an M Audio interface will be silent until I re assign the outputs. It defaults to SPDIF because that was what I used back then.
Look at your Master buss first.
Also check in preferences and your Audio set up.