Filter Documents using lookup and aggregation php

Hi, please i need help i’m finding it hard to filter my documents from mongodb atlas using php.
this is my document structure.
Initial Collection

{ _id :6257f1b36d001b68325e709e
    id :2348
    status :1
    album_id :0
    rp_id :33
    lang_id :7
    cat_id : Array ['01010', '42650']
    mp3_thumbnail :"498.jpg"
    cat_name :"men"
}

**

  1. Lookup method1
$ops = [ // (1)
        '$lookup' => [
            'from' => 'tbl_category_try', //collection to join
            'let' => ["catfed" => '$cat_id'], // cat_id field coming from coll1
             'pipeline' => [
                ['$match' => [$id => ['$in' => ['$$catfed'] ] ] ] // $id variable coming from url as argument
                ],
            'as' => 'joinTab1',
        ],
    ];

Error: Returning all records and empty joint array joinTab1

  1. Lookup Method2
$ops = [ // (1)
        '$lookup' => [
            'from' => 'tbl_category_try',
            'let' => ["catfed" => '$cat_id'],
             'pipeline' => [
                ['$match' => ['$expr' => ['$in' => [$id, '$$catfed' ] ] ] ]
                ],
            'as' => 'joinTab1',
        ],
    ];

Error: failed to optimize pipeline :: caused by :: Failed to optimize expression :: caused by :: $in requires an array as a second argument, found: string