Grouping Documents to Single Object in Aggregation Pipeline

Hello Mongo Community,
I have tried to search from multiple collection with $lookup and $facet and the aggregation query is as the follows where keyword is the search Term

let result = await db.collection(c1).aggregate(
    [
        {
            $match:{
                name: keyword
            }
        },
        {
            $group: {
              _id: 0,
              c1: {
                $push: "$$ROOT"
              }
            }
          },
        {
            "$facet": {
      c2: [{
            "$lookup": {
                "from": '$c2',
                "pipeline": [
                  { "$match": { $text: {$search: keyword}} }
                ],
                "as": c2
              }
        }],
      c3: [{
            "$lookup": {
                "from": '$c3',
                "pipeline": [
                  { "$match": { $text: {$search: keyword}} }
                ],
                "as": c3
              }
        }],
        }}, 
        { "$project": {
            "data": {
              "$concatArrays":concatArray
            }
        }},
        {
            $unwind: "$data"
        },
        {
            $replaceRoot:{newRoot: '$data'}
        },
    ]).toArray()

This give the query as the follows

[
  {
    _id: 0,
    c1: [ [Object] ],
    c2: [ [Object] ]
  },
  {
    _id: 0,
    c1: [ [Object] ],
    c3: [ [Object] ]
  }
]

but what I want to do is to give a single object with collectiion as keys which is as follows

{
    _id: 0,
    c1: [ [Object] ],
    c2: [ [Object] ],
    c3: [ [Object] ]
  }

so how can I improve my query?
I have tried to use $group at the last with this syntax

$group:{
_id:"$_id",
c1:{
$push:"$_c1"},
c2:{
$push:"$_c2"},
c3:{
$push:"$_c3"}
}

but this give result on double nested array like this and I have to unwind the every single field.

{
    _id: 0,
    c1: [ [ [Object] ] ],
    c2: [ [ [Object] ] ],
    c3: [ [ [Object] ] ]
}

with $first it give null ( I don’t know why and please let me know if it is okay)
so is there better accumulator or way to achieve the result I have intended. Thanks in advance