You'll have to use an aggregate for this, sadly due to the nature of your needs this is going to be a very "expensive" pipeline to execute. There is no way to avoid iterating over the entire collection and adding the unique keys to the array.

We're going to use $objectToArray to turn metadata into an array, then $unwind it and finally using $group we could save all the unique values.

db.collection.aggregate([
  {
    $project: {
      keys: {
        $map: {
          input: {
            "$objectToArray": "$metadata"
          },
          in: "$$this.k"
        }
      }
    }
  },
  {
    $unwind: "$keys"
  },
  {
    $group: {
      _id: null,
      keys: {
        "$addToSet": "$keys"
      }
    }
  }
])

Mongo Playground

db.collection.aggregate([
       {
         $addFields: {
             metadata: {
                $objectToArray: "$metadata"
             }
          }
       },
      {
         $unwind: "$metadata"
      },
      {
         $group: {
            _id: "distinct",
            dist: {
               $addToSet: "$metadata.k"
            }
         }
      }
  ])

explained:

1. Convert the metadata object to metadata array having the keys as values in k key.
2. Unwind the metadata array of k keys & v values
3. group with addToSet to extract only the distinct k values in the final result.

playground

helpfull javascript onliner from mongo shell option:

 db.collection.find({},{metadata:1,_id:0}).forEach( function(doc) { for (key in doc.metadata) s.push(key); } );uni = Array.from(new Set(s));printjson(uni);
 ["path","name","origin","source","value"]