[{"name":"User name","messages":[{"message":"Message 1","date":"2022-05-12T00:00:00.000Z"},{"message":"Message 2","date":"2022-05-12T00:00:00.000Z"},{"message":"Message 3","date":"2022-05-13T00:00:00.000Z"},{"message":"Message 4","date":"2022-05-13T00:00:00.000Z"},{"message":"Message 5","date":"2022-05-13T00:00:00.000Z"}]}]

db.collection.aggregate([{$unwind:"$messages"},{$group:{_id:"$messages.date",messages:{$push:"$messages"}}},{$project:{_id:0,date:"$_id",messages:1}}])