So I have something I use. It is an Assignment Report and then I utilize groupings to get the information.
The only downside is that there isn't an out-of-box filter for "Other Team IDs" for the assigned to. You will have to use an EXIST filter for that. (Let me know if you need help with that).
The idea is have active assignments (which for us is projects with Current status and task status is not complete OR projects with Current status and issue status is not Closed or Cancelled) and then group by project. The report is then set to show the Summary tab. (We ignore the "count" column).
Here is an example, hope it helps:
