Great question, @Sandrine.
This is possible using Advanced Search, and you can pull a list of the tasks assigned to each person over a set period of time (i.e. the next 7 days) and then sort by assignee to see how much each person has on their plate. This is a premium feature as you noted, and you can see more information about it here: Using Search & Advanced Search in Asana | Product guide • Asana Product Guide. Hope this helps!