[{"type":"TYPE_1","updateTime":"2020-08-24T11:10:43.219+0000"},{"type":"TYPE_1","updateTime":"2020-09-24T11:10:43.219+0000"},{"type":"TYPE_2","updateTime":"2020-09-25T11:10:43.219+0000"}]

db.collection.aggregate([/** Stage 1*/{$group:{_id:"$type",count:{$sum:1},lastUpdate:{"$max":"$updateTime"}}},/** Stage 2*/{$sort:{lastUpdate:-1}},{$group:{_id:null,data:{$push:{type:"$_id",count:"$count"}},lastUpdate:{$first:"$lastUpdate"}}},{$project:{data:{$arrayToObject:{$map:{input:"$data",in:{k:"$$this.type",v:"$$this.count"}}}},lastUpdate:1}},{$addFields:{"data.lastUpdate":"$lastUpdate"}},{"$replaceRoot":{"newRoot":"$data"}}])