[{id:1,name:"My document 1",allItems:[{id:"item1",name:"My item 1"},{id:"item2",name:"My item 2"},{id:"item3",name:"My item 3"}],containers:[{id:"container1",selectedItems:["item3","item1"]},{id:"container2",selectedItems:["item3"]}]}]

db.collection.aggregate([{$match:{"containers.id":"container1"}},{$project:{name:1,container:{$let:{vars:{container:{$arrayElemAt:[{$filter:{input:"$containers",cond:{$eq:["$$this.id","container1"]}}},0]}},in:{id:"$$container.id",selectedItems:{$filter:{input:"$allItems",cond:{$in:["$$this.id","$$container.selectedItems"]}}}}}}}}])