Database
[{"time":NumberLong(1531958400000)},{"time":NumberLong(1531958400001)},{/** 2021-08-01*/"time":NumberLong(1627804764000)},{/** 2021-01-01*/"time":NumberLong(1609487954000)},{/** 2021-01-02*/"time":NumberLong(1609574354000)}]
Query
db.collection.aggregate([{"$addFields":{"parsedDate":{"$toDate":"$time"}}},{"$addFields":{"year":{$year:"$parsedDate"},"nowYear":{$year:new Date()}}},{$match:{$expr:{$eq:["$year","$nowYear"]}}},{$group:{_id:{"$month":"$parsedDate"},count:{$sum:1}}}])