You can use $graphLookup and other useful array operators,

• $match filter that records only have parent_id is null
• $graphLookup to get child records and depth number in depthField level
• $unwind deconstruct children array and allow to not remove empty children
• $sort by depth level field level in descending order
• $group by id field and reconstruct children array

db.collection.aggregate([
  { $match: { parent_id: null } },
  {
    $graphLookup: {
      from: "collection",
      startWith: "$id",
      connectFromField: "id",
      connectToField: "parent_id",
      depthField: "level",
      as: "children"
    }
  },
  {
    $unwind: {
      path: "$children",
      preserveNullAndEmptyArrays: true
    }
  },
  { $sort: { "children.level": -1 } },
  {
    $group: {
      _id: "$id",
      parent_id: { $first: "$parent_id" },
      name: { $first: "$name" },
      type: { $first: "$type" },
      category: { $first: 1 },
      children: { $push: "$children" }
    }
  },

• $addFields now find the nested level children and allocate to its level,
  • $reduce to iterate loop of children array.
  • initialize default field level default value is -1, presentChild is [], prevChild is [] for the conditions purpose
  • $let to initialize fields:
    • prev as per condition if both level are equal then return prevChild otherwise return presentChild
    • current as per condition if both level are equal then return presentChild otherwise []
  • in to return level field and prevChild field from initialized fields
    • presentChild $filter children from prev array and return, merge current objects with children array using $mergeObjects and concat with current array of let using $concatArrays
• $addFields to return only presentChild array because we only required that processed array

  {
    $addFields: {
      children: {
        $reduce: {
          input: "$children",
          initialValue: { level: -1, presentChild: [], prevChild: [] },
          in: {
            $let: {
              vars: {
                prev: {
                  $cond: [
                    { $eq: ["$$value.level", "$$this.level"] },
                    "$$value.prevChild",
                    "$$value.presentChild"
                  ]
                },
                current: {
                  $cond: [{ $eq: ["$$value.level", "$$this.level"] }, "$$value.presentChild", []]
                }
              },
              in: {
                level: "$$this.level",
                prevChild: "$$prev",
                presentChild: {
                  $concatArrays: [
                    "$$current",
                    [
                      {
                        $mergeObjects: [
                          "$$this",
                          {
                            children: {
                              $filter: {
                                input: "$$prev",
                                as: "e",
                                cond: { $eq: ["$$e.parent_id", "$$this.id"] }
                              }
                            }
                          }
                        ]
                      }
                    ]
                  ]
                }
              }
            }
          }
        }
      }
    }
  },
  {
    $addFields: {
      id: "$_id",
      children: "$children.presentChild"
    }
  }
])

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