In order to see if a report is shared with a user you have to find the report, click on the report name and pull up the report, then click Menu, then click Share to see which groups the report is shared with.

It would helpful if a user could do this more easily and see if a report was shared by hovering over the report name in left navigation. Currently in next gen if a user hovers over a report name in the left navigation a pop up displays more information about the report criteria such as report type, report creator, report created date, etc.

If would be very helpful is IBM included content in the report hover about if the report was shared with other users.

In legacy Explore we have a feature similar to this. We display a icon next to the report name that lets a user visually see if the report is locked (not shared with anyone) or shared with other users.