New insight is available - Forms Assigned To Me. All open assigned to the current user forms are visible there. Forms which has the due date in the past are marked with red and the font is bold. Forms for today and in the future are not formatted.
The user can also select the needed record and by using the Complete button - can open the form to complete it.
NOTE: the old Forms Assigned To Me on the Safe Work Manager RC is hidden and marked as obsolete in the code.