range_date_to_rows.sql

select id,
       start_at,
#        date_add(start_at, interval -DAY(start_at) + 1 DAY),
       end_at
from sample_data;

# [
#   {
#     "id": 1,
#     "start_at": "2022-04-01 20:57:07",
#     "end_at": "2022-07-26 20:57:21"
#   },
#   {
#     "id": 2,
#     "start_at": "2022-03-04 20:57:07",
#     "end_at": "2022-03-26 20:57:21"
#   },
#   {
#     "id": 3,
#     "start_at": "2022-06-16 20:57:07",
#     "end_at": "2022-07-20 20:57:07"
#   }
# ]


select id, date_format(month, '%Y%m')
from sample_data
         # 区切りたい日付単位のテーブルとinner joinで掛け算状態にする
         inner join (SELECT '2022-03-01' as month
                     UNION
                     SELECT '2022-04-01' as month
                     UNION
                     SELECT '2022-05-01' as month
                     UNION
                     SELECT '2022-06-01' as month
                     UNION
                     SELECT '2022-07-01' as month) as months
                    on month
                        between
                        # monthsが月初めの日付なので、start_atの月初日を取得する
                        DATE(date_add(start_at, interval -DAY(start_at) + 1 DAY))
                        and end_at
order by id, month asc
;
# [
#   {
#     "id": 1,
#     "date_format(month, '%Y%m')": "202204"
#   },
#   {
#     "id": 1,
#     "date_format(month, '%Y%m')": "202205"
#   },
#   {
#     "id": 1,
#     "date_format(month, '%Y%m')": "202206"
#   },
#   {
#     "id": 1,
#     "date_format(month, '%Y%m')": "202207"
#   },
#   {
#     "id": 2,
#     "date_format(month, '%Y%m')": "202203"
#   },
#   {
#     "id": 3,
#     "date_format(month, '%Y%m')": "202206"
#   },
#   {
#     "id": 3,
#     "date_format(month, '%Y%m')": "202207"
#   }
# ]

see https://stackoverflow.com/a/54068381