Hi Lars
its best to think of Teams as a holding area before a task is assigned. It is meant to be used as a place for a team to see what work is assigned to them, and then eventually choose one of them to do the task.
There is no way to assign a group of people to a task and have it show up on their task list that I have found but I’m hoping someone will have a clever answer to this so I want to follow this thread as I find it frustrating as well. I’m sure in this forum I have asked this same question.
What I do is assign all the people to the task if it’s a task the entire group needs to Complete. For example, there are projects where every person on a team needs to review a proof and they need advance notice when it will be coming so that task has 10 people assigned to it so it shows up in their task list.