remove the product from the shopping cart session by product_id in laravel

How do I remove the product from the shopping cart session by product_id? I've sent the product ID to the controller using Ajax . These are my codes and this is the structure of my shopping cart session

json structure of session :

[{"product_id":"2","quantity":5,"userId":"1","product_name":"\u062f\u0645\u067e\u0627\u06cc\u06cc \u0627\u0628\u0631\u06cc ","product_root":"files\\courses\\course2","product_description":"\u062f\u0645\u067e\u0627\u06cc\u06cc \u0627\u0628\u0631\u06cc ","product_price":5000},{"product_id":"1","quantity":1,"userId":"1","product_name":"\u062a\u0645\u0628\u0648\u0646 \u06cc\u0632\u062f\u06cc\u0645 \u0645\u0627\u0644 \u062a\u0648 ","product_root":"files\\courses\\course1","product_description":"asdasdasdasdsadsadsadas","product_price":1000}]

controller function :

public function deleteCardItem(Request $request)
{
    $product_id = $request-> id;
    $cards = session()->get('cards');
    $ids = array_column($cards, 'product_id');
    $index = array_search($product_id, $ids);
    unset($cards[$index]);
}

ajax :

          $.ajax({
                type: 'post',
                url: '',
                data: {
                    'id':Product_id,
                    'userId':'',
                    "_token": '',
                },
                cache: false,
                success: function(res){
                }
            });

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