Database

[{_id:"...",name:"myName",versions:{"1.0.0":{status:"unpublished"},"1.0.1":{status:"published"},"2.2.0":{status:"unpublished"},"14.3023.1":{status:"published"}}}]

Query

db.collection.aggregate([{$match:{name:"myName"}},{"$addFields":{"versions":{"$objectToArray":"$versions"}}},{"$addFields":{"versions":{"$filter":{"input":"$versions","as":"ver","cond":{$eq:["$$ver.v.status","published"]}}}}},{"$addFields":{"versions":{"$arrayToObject":"$versions"}}}])

Result