Database

db={employees:[{"_id":"621eedae92979fd8f0e9451d","name":"Pallab Koley","shifts":{"_id":"62636b9fcbda6d2b17f5cae0","month":"2022-05","shift":[{"date":"2022-05-01","shiftId":"622bb0f4b88dc92e3c2cac56"},{"date":"2022-05-02","shiftId":"622b55f8f59dcdd1ab9b36b1"}]}},{"_id":"62626a7446ba9a911a623b37","name":"Pinki Das","shifts":{"_id":"62636ba4cbda6d2b17f5cae1","month":"2022-05","shift":[{"date":"2022-05-01","shiftId":"622bb0f4b88dc92e3c2cac56"}]}}],shifts:[{_id:"622bb0f4b88dc92e3c2cac56",name:"Day"},{_id:"622b55f8f59dcdd1ab9b36b1",name:"Morning"}]}

Query

db.employees.aggregate([{$lookup:{from:"shifts",localField:"shifts.shift.shiftId",foreignField:"_id",as:"shifts.shift2"}},{$set:{"shifts.shift":{$map:{input:"$shifts.shift",as:"s",in:{$mergeObjects:["$$s",{shiftId:{$filter:{input:"$shifts.shift2",as:"s2",cond:{$eq:["$$s2._id","$$s.shiftId"]}}}}]}}}}},{$unset:["shifts.shift2"]}])

Result