Cannot get parent data by mongoDB aggregate graphLookup

Following is the data

[
  {
    "_id": {
      "$oid": "6364f2eee35fc06fa06afb5f"
    },
    "type": "subbranch",
    "parent_id": "635116c18fe4294398842ebb",
    "org_name": "Pune - Delhi"
  },
  {
    "_id": {
      "$oid": "635116c18fe4294398842ebb"
    },
    "type": "branch",
    "org_name": "Delhi Branch",
    "parent_id": "0"
  }
]

query which i have written is as follows

// req.params.id is 6364f2eee35fc06fa06afb5f
let id = mongoose.Types.ObjectId(req.params.id);
        let data = await organisation.aggregate([
            {
                $addFields: { "_idString": { "$toString": "$_id" }}
            },
            {
                $graphLookup: {
                   from: "organisations",
                   startWith: "$parent_id",
                   connectFromField: "parent_id",
                   connectToField: "_idString",
                   as: "parent"
                }
            },
            {
                $match: {_id: id}
            },
        ]);

but in output i get as follow

[
  {
    "_id": "6364f2eee35fc06fa06afb5f",
    "type": "subbranch",
    "parent_id": "635116c18fe4294398842ebb",
    "org_name": "Pune - Delhi",
    "_idString": "6364f2eee35fc06fa06afb5f",
    "parent": [

    ]
  }
]

i am getting empty parent array but expected output is array with parent data in it. any suggestion would be appreciated.

Remember connectFromField expected or extracted from current aggregated collection while connectToField is connected to from orginal collection

DEMO ON https://mongoplayground.net/p/vYDdOgNt9bW

The aggregate query be like

db.collection.aggregate([
  {
    $addFields: {
      "parent_id": {
        $convert: {
          input: "$parent_id",
          to: "objectId",
          onError: "$parent_id",
        }
      }
    }
  },
  {
    $graphLookup: {
      from: "collection",
      startWith: "$parent_id",
      connectFromField: "parent_id",
      connectToField: "_id",
      as: "parent"
    }
  }
])

Outputs

[
  {
    "_id": ObjectId("6364f2eee35fc06fa06afb5f"),
    "org_name": "Pune - Delhi",
    "parent": [
      {
        "_id": ObjectId("635116c18fe4294398842ebb"),
        "org_name": "Delhi Branch",
        "parent_id": "0",
        "type": "branch"
      }
    ],
    "parent_id": ObjectId("635116c18fe4294398842ebb"),
    "type": "subbranch"
  },
  {
    "_id": ObjectId("635116c18fe4294398842ebb"),
    "org_name": "Delhi Branch",
    "parent": [],
    "parent_id": "0",
    "type": "branch"
  }
]