How to group this using aggregation

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1

I have array

"permissions": [
            {
                "module": "transactions",
                "sub_module": [
                    {
                        "name": "health",
                        "headers": [
                            {
                                "header_id": "651526995487452392fba692",
                                "status": true,
                                "_id": "65153030866481f26ac30f13"
                            },
                            {
                                "header_id": "651526a75487452392fba695",
                                "status": true,
                                "_id": "65153030866481f26ac30f14"
                            },
                            {
                                "header_id": "651526ac5487452392fba698",
                                "status": true,
                                "_id": "65153030866481f26ac30f15"
                            },
                            {
                                "header_id": "651526b25487452392fba69b",
                                "status": true,
                                "_id": "65153030866481f26ac30f16"
                            },
                            {
                                "header_id": "651526c85487452392fba69e",
                                "status": false,
                                "_id": "65153030866481f26ac30f17"
                            }
                        ]
                    }
                ]
            },
            {
                "module": "dashbord",
                "sub_module": [
                    {
                        "name": "health",
                        "headers": [
                            {
                                "header_id": "651526995487452392fba692",
                                "status": true,
                                "_id": "65153030866481f26ac30f0d"
                            },
                            {
                                "header_id": "651526a75487452392fba695",
                                "status": true,
                                "_id": "65153030866481f26ac30f0e"
                            },
                            {
                                "header_id": "651526ac5487452392fba698",
                                "status": true,
                                "_id": "65153030866481f26ac30f0f"
                            },
                            {
                                "header_id": "651526b25487452392fba69b",
                                "status": true,
                                "_id": "65153030866481f26ac30f10"
                            },
                            {
                                "header_id": "651526c85487452392fba69e",
                                "status": false,
                                "_id": "65153030866481f26ac30f11"
                            }
                        ]
                    },
                    {
                        "name": "car",
                        "headers": [
                            {
                                "header_id": "651526995487452392fba692",
                                "status": true,
                                "_id": "65153030866481f26ac30f0d"
                            },
                            {
                                "header_id": "651526a75487452392fba695",
                                "status": true,
                                "_id": "65153030866481f26ac30f0e"
                            },
                            {
                                "header_id": "651526ac5487452392fba698",
                                "status": true,
                                "_id": "65153030866481f26ac30f0f"
                            },
                            {
                                "header_id": "651526b25487452392fba69b",
                                "status": true,
                                "_id": "65153030866481f26ac30f10"
                            },
                            {
                                "header_id": "651526c85487452392fba69e",
                                "status": false,
                                "_id": "65153030866481f26ac30f11"
                            }
                        ]
                    }
                ]
            }
        ]
````Preformatted text`

i want like this

"permissions": [
    {
        "module": "transactions",
        "sub_module": [
            {
                "name": "health",
                "headers": [
                    {
                        "name": "view",
                        "status": true,
                        "_id": "65153030866481f26ac30f13"
                    },
                    {
                        "name": "add",
                        "status": true,
                        "_id": "65153030866481f26ac30f14"
                    },
                    {
                        "name": "edit",
                        "status": true,
                        "_id": "65153030866481f26ac30f15"
                    },
                    {
                        "header_id": "remove",
                        "status": true,
                        "_id": "65153030866481f26ac30f16"
                    },
                    {
                        "name": "download",
                        "status": false,
                        "_id": "65153030866481f26ac30f17"
                    }
                ]
            }
        ]
    },
    {
        "module": "dashbord",
        "sub_module": [
            {
                "name": "health",
                "headers": [
                    {
                        "name": "view",
                        "status": true,
                        "_id": "65153030866481f26ac30f0d"
                    },
                    {
                        "name": "add",
                        "status": true,
                        "_id": "65153030866481f26ac30f0e"
                    },
                    {
                        "name": "edit",
                        "status": true,
                        "_id": "65153030866481f26ac30f0f"
                    },
                    {
                        "name": "remove",
                        "status": true,
                        "_id": "65153030866481f26ac30f10"
                    },
                    {
                        "header_id": "download",
                        "status": false,
                        "_id": "65153030866481f26ac30f11"
                    }
                ]
            },
            {
                "name": "car",
                "headers": [
                    {
                        "name": "view",
                        "status": true,
                        "_id": "65153030866481f26ac30f0d"
                    },
                    {
                        "name": "add",
                        "status": true,
                        "_id": "65153030866481f26ac30f0e"
                    },
                    {
                        "name": "edit",
                        "status": true,
                        "_id": "65153030866481f26ac30f0f"
                    },
                    {
                        "name": "remove",
                        "status": true,
                        "_id": "65153030866481f26ac30f10"
                    },
                    {
                        "name": "download",
                        "status": false,
                        "_id": "65153030866481f26ac30f11"
                    }
                ]
            }
        ]
    }
]
````Preformatted text`

to fetch name of header use header_id from header table

3

Have you tried $lookup?

But you do one thing really wrong. You store you id as string rather than a real object id. This takes more space and you would need to convert to object id every time you lookup.