Use array values as path to match documents in mongodb

Given a list of documents like:

[
  {
    _id: 1,
    field: {
      subfield1: {
        subsubfield1: [
          "value",
          "test"
        ]
      },
      subfield2: {
        subsufield2: [
          "value"
        ]
      }
    },
    paths: [
      "field.subfield1.subsubfield1",
      "field.subfield2.subsubfield2"
    ]
  },
  {
    _id: 2,
    field: {
      subfield1: {
        subsubfield1: [
          "value"
        ]
      },
      subfield2: {
        subsufield2: [
          "value",
          "test"
        ]
      }
    },
    paths: [
      "field.subfield2.subsubfield2"
    ]
  },
  {
    _id: 3,
    field: {
      subfield1: {
        subsubfield1: [
          "value"
        ]
      },
      subfield2: {
        subsufield2: [
          "value"
        ]
      }
    },
    paths: [
      "field.subfield1.subsubfield1"
    ]
  },
  {
    _id: 4,
    field: {
      subfield1: {
        subsubfield1: [
          "value"
        ]
      },
      subfield2: {
        subsufield2: [
          "value"
        ]
      }
    },
    paths: [
      "field.subfield1.subsubfield1"
      "field.subfield2.subsubfield2"
    ]
  }
]

in which paths field is an array with paths to document. I have to return documents that have test as a value in at least one of the paths specified in the paths array. For example, the documents with _id 1 and _id 2 would be returned, because at least one of the values in paths is a path in the document with value test. Documents with _id 3 and _id 4 are not returned since no element of paths is a path in the document that has value test.

EDIT: since OP updated the assumption that the field is always nested in 3 levels. This actually simplify the scenario, and thus the aggregation pipeline.

1. use $objectToArray to parse the field object as an array of k-v tuple, named parsed
   • use $map to iterate through the parsed array
   • slightly wrangle the k to append the field. as prefix
2. repeat the parsing
3. $match only if any element in parsed array are inside the paths array and have value test

db.collection.aggregate([
  {
    "$set": {
      "parsed": {
        "$map": {
          "input": {
            "$objectToArray": "$field"
          },
          "as": "kv",
          "in": {
            k: {
              "$concat": [
                "field",
                ".",
                "$$kv.k"
              ]
            },
            v: "$$kv.v"
          }
        }
      }
    }
  },
  {
    "$set": {
      "parsed": {
        "$reduce": {
          "input": "$parsed",
          "initialValue": [],
          "in": {
            "$concatArrays": [
              "$$value",
              {
                "$map": {
                  "input": {
                    "$objectToArray": "$$this.v"
                  },
                  "as": "kv",
                  "in": {
                    k: {
                      "$concat": [
                        "$$this.k",
                        ".",
                        "$$kv.k"
                      ]
                    },
                    v: "$$kv.v"
                  }
                }
              }
            ]
          }
        }
      }
    }
  },
  {
    "$match": {
      "$expr": {
        "$anyElementTrue": {
          "$map": {
            "input": "$parsed",
            "as": "p",
            "in": {
              //1. matching
              "$and": [
                // 1.1 matching path
                {
                  "$in": [
                    "$$p.k",
                    "$paths"
                  ]
                },
                // 1.2 matching value "test"
                {
                  "$in": [
                    "test",
                    "$$p.v"
                  ]
                }
              ]
            }
          }
        }
      }
    }
  }
])

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