[{"data":{"2018-05-11":{"12":12.4,"00":11.3},"2018-12-31":{"12":12.4,"06":13},"2021-05-10":{"00":11.3,"06":13},"2021-05-11":{"12":12.4,"00":11.3,"06":13},"2021-05-13":{"12":6,"06":13},"2020-06-01":{"12":3.4,"09":1.8},"2020-06-15":{"12":3.9,"09":11.8}}}]

db.collection.aggregate([{$project:{data:{$arrayToObject:{$filter:{input:{$objectToArray:"$data"},cond:{$and:[{$in:[{$year:{$toDate:"$$this.k"}},[2021]]},{$in:[{$month:{$toDate:"$$this.k"}},[5]]}]}}}}}}])