如何在mongoose中编写只返回嵌套数组中匹配的对象Id的查询？

const mongoose = require('mongoose');

const schema = new mongoose.Schema({
  nestedArray: [{
    objectId: {
      type: mongoose.Schema.Types.ObjectId,
      required: true
    }
  }]
});

const Model = mongoose.model('Model', schema);

async function findMatchingObjects() {
  const result = await Model.aggregate([
    {
      $match: {
        nestedArray: {
          $elemMatch: {
            objectId: { $eq: 'your_matching_object_id' }
          }
        }
      }
    },
    {
      $project: {
        matchedIds: {
          $map: {
            input: '$nestedArray',
            as: 'item',
            in: {
              $cond: [
                { $eq: ['$$item.objectId', 'your_matching_object_id'] },
                '$$item.objectId',
                false
              ]
            }
          }
        }
      }
    }
  ]);

  console.log(result);
}

findMatchingObjects();