One of my biggest pet peeves about Canvas is the ambiguity of the word "group." In Canvas, the term "group" means a "team" of students who are collaborating together. The Infrastructure developers should have used the word "team" from the get-go.
What you want to do is create "sections." Then you can easily assign "sections" of students to do differentiated work. The students in the "sections" will work individually, and they will not see who is in their "section."
So, just how do we get the Infrastructure development team to improve their use of terminology? That's the million dollar question.