[{"id":1,"period":[{"startDate":"2020-05-05","endDate":"2020-05-06"},{"startDate":"2020-06-05","endDate":"2020-06-06"}]},{"id":2,"period":[{"startDate":"2024-07-05","endDate":"2024-07-06"},{"startDate":"2024-08-05","endDate":"2024-08-06"}]}]

db.collection.aggregate([{$project:{_id:0,id:1,minDate:{$dateFromString:{dateString:{$reduce:{input:"$period",initialValue:{$first:"$period.startDate"},in:{$min:["$$value","$$this.startDate"]}}}}},maxDate:{$dateFromString:{dateString:{$reduce:{input:"$period",initialValue:{$first:"$period.endDate"},in:{$max:["$$value","$$this.startDate"]}}}}}}},{$group:{_id:0,startDateLargerIds:{$push:{$cond:[{$gt:["$minDate",ISODate("2022-08-03T11:37:03.954Z")]},"$id","$$REMOVE"]}},endDateSmallerIds:{$push:{$cond:[{$lt:["$maxDate",ISODate("2022-08-03T11:37:03.954Z")]},"$id","$$REMOVE"]}}}},{$unset:"_id"}])