Limit graphLookup with matching the "from" side in MongoDB

Question

I have a MongoDB collection where the documents are stored in a hierarchy and each node has a specific set of values assigned to them:

Document {
  _id: ObjectId
  parentId: ObjectId
  values [ { name: string, value: number } ]
  valueCalculationType: "Manual" | "SumOfChildren"
}

What is interesting is that a node (document) can have their values specified manually (valueCalculationType is "Manual"), or it can be a linear sum of their children (the exact logic is explained below). This is a recursive algorythm where calculating the values for each node with $graphLookup seems a good fit.

At first glance I thought that my algorythm would be to do a graphLookup through all children and then sum up the value from all descendants with the "Manual" type.

$graphLookup: {
  from: 'nodes',
  startWith: '$_id',
  connectFromField: '_id',
  connectToField: 'parentId',
  as: 'descendants',
},

// The summarizing is omitted, but could be done in business logic.

The issue here is that nodes can have a "Manual" type and still have children, meaning that their children are not needed to be summed up, and that subtree should be cut off from the calculation. This means I would have to omit nodes where the parent is "Manual". I know about the restrictSearchWithMatch property, but I'm only able to match for the current node with it, so a "Do not include nodes if parent is Manual" is not directly possible.

What I could come up with is these:

1. Load all descendants and build a tree from the elements in business logic - this would be a quite annoying solution, but as a last resort I could use that.
2. Load all descendants with $graphLookup that have the valueCalculationType: SumOfChildren in an array in one aggregation (so it won't get into manual subtrees), and in a next aggregation step use a $lookup to load all valueCalculationType: Manual children of the first aggregation's output list property. This would mean that the second aggregation result property should contain "Manual" descendants that only have "SumOfChildren" ancestors, but I'm not sure how to do this:

[
  {
    $graphLookup: {
      from: 'nodes',
      startWith: '$_id',
      connectFromField: '_id',
      connectToField: 'parentId',
      restrictSearchWithMatch: { $valueCalculationType: "SumOfChildren" },
      as: 'sumOfChildrenDescendants',
    }
  },
  {
    $lookup: {
      from: "nodes",
      as: "manualDescendants",
      pipeline: [
        { 
          $match: {
            valueCalculationType: 'Manual',
            parentId: "I don't know"
          }
        },
      ]
    }
  }
]

The second $lookup's match is not something I understand how to do.