It is great to hear about the support of your university! Studying in foreign countries is something privileged. I hope you will get a good job at home easily.
Opening Unity either presents you a dialog where you can select an existing project or create a new one, or Unity editor opens directly e.g. with the last project you were editing. Make sure that you are using the correct version of Unity - it should match with the game's.
Have a good journey back home, and all the best from my family and me!