Hi @BronwynJackson ...
There isn't anything in Canvas terminology called an "Assessment Group" as you are referring. However, what I think you are asking about is "Assignment Groups" via your "Assignments" index page. "Assignment Groups" allow you to organize your assignments (such as all quizzes together, all written work together, etc.). And, if you want, you can then weight those "Assignment Groups" using percentages for grading purposes.
I don't really think you need to use Commons to do what you are asking. Why not just copy the assignments directly from one course to another without creating the extra work of having to go through Commons? You'd want to log in to the course where you want the "Assignment Group" to be imported into. Then, follow the steps in How do I select specific content as part of a course import?. During these steps, you'll be selecting the course where the "Assignment Group" already exists. Then, when it comes time to choose which content from your course you want to import by clicking on the "Select Content" button, you'll see an arrow pointing to the right next to the row "Assignments". Click on that arrow so it points down. You should then see all of the "Assignment Groups" listed. Place a checkmark next to the name of the "Assignment Group" that you want to import into your new course. (You can even click the arrow to expand that folder to confirm all assignments are there.) Then, click the "Select Content" button at the bottom.
Hopefully, this will copy all assignments into your course...and also carry over the "Assignment Group" as well. I hope this helps!
