MySQL Finding intersection where 2 entered dates intersect between a start_date and end_date

You can find intersections if start_date is less than the max of the 2 dates and end_date is greater than the min of the 2 dates:

WHERE r.end_date >= '2022-02-28 08:30:00'
  AND r.start_date <= '2022-02-28 12:30:00'