Database
db={"teacher":[{"id":1276,"start_time":"2023-03-22T07:00:25.787Z","end_time":"2023-03-22T10:00:35.604Z",},{"id":1564,"start_time":"2023-03-22T07:00:25.787Z","end_time":"2023-03-22T10:00:35.604Z",},{"id":1276,"start_time":"2023-03-22T011:00:25.787Z","end_time":"2023-03-22T15:00:35.604Z",}]}
Query
db.teacher.aggregate([{$match:{id:1276}},{$addFields:{overlap:{$and:[{$lte:["$start_time","2023-03-22T011:00:24.787Z"]},{$gte:["$end_time","2023-03-22T10:00:35.604Z"]}]}}},{$group:{_id:"$id",overlap:{$push:"$overlap"}}},{$addFields:{overlap:{$in:[true,"$overlap"]}}}])