I’d have to see your assignment response to make recommendations! And I probably shouldn’t print my recommendations here publicly, as this company probably wants to keep the assignment confidential. Feel free to befriend me on LinkedIn, and I'll take a look at your assignment and give you feedback.
Ideally, it's a combination of the GM, product management and product marketing. The GM would set the overall business goals for the year or quarter including revenue. The PM often drives the product launch adoption and revenue goals for that product. PMM often builds the plan with the metrics to help back into those goals.
The important thing is that if you see a gap, make sure that someone is owning all of these goals, otherwise, it will be meaningless to have launch metrics.