Lookup not using correct index

The aggregation below actually occurs inside of a lookup but for having the explain for it I am running it alone (not in the lookup).
The problem is that it is running super slow (more than 200 seconds) because it is not using the correct index. I tried several things but it still uses wrong index.

The explain

{
    "stages" : [ 
        {
            "$cursor" : {
                "query" : {
                    "$expr" : {
                        "$and" : [ 
                            {
                                "$eq" : [ 
                                    "$contact_id", 
                                    ObjectId("5fadca37b32109095e324434")
                                ]
                            }, 
                            {
                                "$eq" : [ 
                                    "$channel", 
                                    "form"
                                ]
                            }, 
                            {
                                "$eq" : [ 
                                    "$event", 
                                    "submitted"
                                ]
                            }, 
                            {
                                "$eq" : [ 
                                    "$form_id", 
                                    ObjectId("6000194aae91a5ea3fa9975b")
                                ]
                            }
                        ]
                    }
                },
                "fields" : {
                    "channel" : 1,
                    "contact_id" : 1,
                    "event" : 1,
                    "form_id" : 1,
                    "_id" : 0
                },
                "queryPlanner" : {
                    "plannerVersion" : 1,
                    "namespace" : "production.events",
                    "indexFilterSet" : false,
                    "parsedQuery" : {
                        "$and" : [ 
                            {
                                "$expr" : {
                                    "$and" : [ 
                                        {
                                            "$eq" : [ 
                                                "$contact_id", 
                                                {
                                                    "$const" : ObjectId("5fadca37b32109095e324434")
                                                }
                                            ]
                                        }, 
                                        {
                                            "$eq" : [ 
                                                "$channel", 
                                                {
                                                    "$const" : "form"
                                                }
                                            ]
                                        }, 
                                        {
                                            "$eq" : [ 
                                                "$event", 
                                                {
                                                    "$const" : "submitted"
                                                }
                                            ]
                                        }, 
                                        {
                                            "$eq" : [ 
                                                "$form_id", 
                                                {
                                                    "$const" : ObjectId("6000194aae91a5ea3fa9975b")
                                                }
                                            ]
                                        }
                                    ]
                                }
                            }, 
                            {
                                "channel" : {
                                    "$_internalExprEq" : "form"
                                }
                            }, 
                            {
                                "contact_id" : {
                                    "$_internalExprEq" : ObjectId("5fadca37b32109095e324434")
                                }
                            }, 
                            {
                                "event" : {
                                    "$_internalExprEq" : "submitted"
                                }
                            }, 
                            {
                                "form_id" : {
                                    "$_internalExprEq" : ObjectId("6000194aae91a5ea3fa9975b")
                                }
                            }
                        ]
                    },
                    "queryHash" : "F1331520",
                    "planCacheKey" : "0C213055",
                    "winningPlan" : {
                        "stage" : "FETCH",
                        "filter" : {
                            "$and" : [ 
                                {
                                    "$expr" : {
                                        "$and" : [ 
                                            {
                                                "$eq" : [ 
                                                    "$contact_id", 
                                                    {
                                                        "$const" : ObjectId("5fadca37b32109095e324434")
                                                    }
                                                ]
                                            }, 
                                            {
                                                "$eq" : [ 
                                                    "$channel", 
                                                    {
                                                        "$const" : "form"
                                                    }
                                                ]
                                            }, 
                                            {
                                                "$eq" : [ 
                                                    "$event", 
                                                    {
                                                        "$const" : "submitted"
                                                    }
                                                ]
                                            }, 
                                            {
                                                "$eq" : [ 
                                                    "$form_id", 
                                                    {
                                                        "$const" : ObjectId("6000194aae91a5ea3fa9975b")
                                                    }
                                                ]
                                            }
                                        ]
                                    }
                                }, 
                                {
                                    "form_id" : {
                                        "$_internalExprEq" : ObjectId("6000194aae91a5ea3fa9975b")
                                    }
                                }
                            ]
                        },
                        "inputStage" : {
                            "stage" : "IXSCAN",
                            "keyPattern" : {
                                "contact_id" : NumberLong(1),
                                "channel" : NumberLong(1),
                                "campaign_id" : NumberLong(1),
                                "event" : NumberLong(1)
                            },
                            "indexName" : "contact_id_1_channel_1_campaign_id_1_event_1",
                            "isMultiKey" : false,
                            "multiKeyPaths" : {
                                "contact_id" : [],
                                "channel" : [],
                                "campaign_id" : [],
                                "event" : []
                            },
                            "isUnique" : false,
                            "isSparse" : false,
                            "isPartial" : false,
                            "indexVersion" : 2,
                            "direction" : "forward",
                            "indexBounds" : {
                                "contact_id" : [ 
                                    "[ObjectId('5fadca37b32109095e324434'), ObjectId('5fadca37b32109095e324434')]"
                                ],
                                "channel" : [ 
                                    "[\"form\", \"form\"]"
                                ],
                                "campaign_id" : [ 
                                    "[MinKey, MaxKey]"
                                ],
                                "event" : [ 
                                    "[\"submitted\", \"submitted\"]"
                                ]
                            }
                        }
                    },
                    "rejectedPlans" : [ 

...

    ],
    "serverInfo" : {
        "host" : "atlas-lfb6fy-shard-00-02.pdned.mongodb.net",
        "port" : 27017,
        "version" : "4.2.13",
        "gitVersion" : "82dd40f60c55dae12426c08fd7150d79a0e28e23"
    },
    "ok" : 1.0,
    "$clusterTime" : {
        "clusterTime" : Timestamp(1620401634, 7),
        "signature" : {
            "hash" : { "$binary" : "1E2/PFKIKQ3NL5Gqk+kJmhjjUoA=", "$type" : "00" },
            "keyId" : NumberLong(6902231878846119939)
        }
    },
    "operationTime" : Timestamp(1620401634, 7)
}

I cutted the explain because it was too long but the fact is the index “contact_id_1_channel_1_form_id_1_event_1” is in the rejected plans.

How to use it?