Performance of $lookup in aggregation

Working with Data
1

Hi Everyone!
I have 2 collections:
Query Collection

[
  {
    _id: "66bc7e0cbc5dcf3b76f3f55e",
    query: "wrapper"
  }
]

and the BigData collection contains large data.

I have a question about comparing the performance of the following two commands:

The first command:

db.BigData.aggregate([
  {
    $match: {
      key1: "condition1"
    }
  },
  {
    $limit: 25
  },
  {
    $project: {
      ...
    }
  }
])

The second command:

db.Query.aggregate([
  {
    $limit:1
  },
  {
    $set: {
      "success": true
    }
  },
  {
    $lookup: {
      from: "BigData",
      pipeline: [
        {
          $match: {
            key1: "condition1"
          }
        },
        {
          $limit: 25
        },
        {
          $project: {
            ...
          }
        }
      ],
      as: "data"
    }
  }
])

Are the performance of these two commands equivalent?
If they are equivalent in performance, is using multiple nested $lookup operations in the second command an optimal solution for join documents? If the performance is different, how should I query to optimize it?
I prefer to use the second command because I want all query commands to return data in a specific structure:

{
  success: true,
  data: [],
  totalCount: "pipeline Count based on a complex condition"
}

The second command returns an array instead of a single object as I need. Can you help me modify the command to return the result as a single object in the most optimal way for large data?

Thanks in advance!