WITH date_range AS (
  SELECT
    TIMESTAMP '2023-03-15 09:20:00' AS start_time,
    TIMESTAMP '2023-03-15 13:05:00' AS end_time
),
hour_range AS (
  SELECT
    date_trunc('hour', start_time) + (n - 1) * INTERVAL '1 hour' AS hour_start,
    date_trunc('hour', start_time) + n * INTERVAL '1 hour' - INTERVAL '1 second' AS hour_end
  FROM date_range, generate_series(1, CEIL(EXTRACT(epoch FROM (end_time - start_time))/3600)::integer + 1) AS n
)
SELECT
  CASE
    WHEN start_time > hour_start THEN start_time
    ELSE hour_start
  END AS start_time,
  CASE
    WHEN end_time < hour_end THEN end_time
    ELSE hour_end
  END AS end_time
FROM date_range, hour_range
WHERE hour_start < end_time
ORDER BY start_time;

SELECT GREATEST(start_time, dt) s
     , LEAST(end_time, dt + INTERVAL '1 HOUR' - INTERVAL '1 SECOND') end_time
  FROM (SELECT TIMESTAMP '2023-03-15 09:20:00' start_time
             , TIMESTAMP '2023-03-15 13:05:00' end_time
        ) a
     , GENERATE_SERIES(DATE_TRUNC('HOUR', start_time), end_time, INTERVAL '1 HOUR') dt
;