Modify nested object using jsonata and return the whole object

Question

This is the input object :

{
    "items": [{}],
    "modular_content": {
      "first_child_b": {
        "elements": {
          "subpages": {
            "type": "modular_content",
            "name": "Children Pages",
            "value": ["second_child_b"]
          }
        }
      },
      "second_child_b": {
        "elements": {
          "subpages": {
            "type": "modular_content",
            "name": "Children Pages",
            "value": []
          }
        }
      },
      "top_level_b": {
        "elements": {
          "subpages": {
            "type": "modular_content",
            "name": "Children Pages",
            "value": ["first_child_b"]
          }
        }
      }
    }
  }

This is my expected response:

{
  items: [ {} ],
  modular_content: {
    first_child_b: {
      elements: {
        subpages: {
          type: 'modular_content',
          name: 'Children Pages',
          value: [ 'second_child_b' ],
          data: [
            {
              elements: {
                subpages: {
                  type: 'modular_content',
                  name: 'Children Pages',
                  value: [],
                  data: []
                }
              }
            }
          ]
        }
      }
    },
    second_child_b: {
      elements: {
        subpages: {
          type: 'modular_content',
          name: 'Children Pages',
          value: [],
          data: []
        }
      }
    },
    top_level_b: {
      elements: {
        subpages: {
          type: 'modular_content',
          name: 'Children Pages',
          value: [ 'first_child_b' ],
          data: [
            {
              elements: {
                subpages: {
                  type: 'modular_content',
                  name: 'Children Pages',
                  value: [ 'second_child_b' ],
                  data: [
                    {
                      elements: {
                        subpages: {
                          type: 'modular_content',
                          name: 'Children Pages',
                          value: [],
                          data: []
                        }
                      }
                    }
                  ]
                }
              }
            }
          ]
        }
      }
    }
  }
}

Basically, if the subpage value array has some value and it is present in the modular_content object, I want to append it inside the parent object.

This is my jsonata expression

(
    $hasProperty := function ($obj, $field){
        $lookup($obj, $field)? true: false
    };

    $nestSubpages := function ($field) {
        $hasProperty(modular_content, $field)?
        (
            $subPageValue := $lookup(modular_content, $field).elements.subpages.value;
            $nestedSubpages := $map($subPageValue, function($subPage){$nestSubpages($subPage)});
            $ ~> | $lookup(modular_content, $field).elements.subpages| { "data" : $nestedSubpages } |
        )
            :
            {}
    };
    
    $each(modular_content, function ($v, $k){
        $nestSubpages($k)
    })
)

https://try.jsonata.org/NtyRb5A9z In this expression, the whole input object is embedded instead of only the child object. Also, this returns an array of objects (1 obj for each key).