Why is the item not being added to the Django cart?

Question

Django

The product is not added to the cart, although the links are correct, tell me what's the problem? I pass from another application shop?, the link works, but the addition does not occur.
urls.py

from django.urls import path, include
from . import views

app_name='cart'

urlpatterns = [
    path('add/<int:product_id>/', views.cart_add, name='cart_add'),
    path('remove/<int:product_id>/', views.cart_remove, name='cart_remove'),
    path('', views.cart_detail, name='cart_detail'),
]

views.py
from django.shortcuts import render, redirect, get_object_or_404
from django.views.decorators.http import require_POST
from shop.models import Product, Category
from .cart import Cart
from .forms import CartAddProductForm


@require_POST
def cart_add(request, product_id):
    cart = Cart(request)
    product = get_object_or_404(Product, id=product_id)
    form = CartAddProductForm(request.POST)
    if form.is_valid():
        cd = form.cleaned_data
        cart.add(product=product,
                 quantity=cd['quantity'],
                 update_quantity=cd['update'])
    return redirect('cart:cart_detail')

def cart_remove(request, product_id):
    cart = Cart(request)
    product = get_object_or_404(Product, id=product_id)
    cart.remove(product)
    return redirect('cart:cart_detail')

def cart_detail(request):
    cart = Cart(request)
    categories= Category.objects.all()
    return render(request, 'cart/detail.html', {'cart': cart,'categories':categories})

forms.py

from django import forms

PRODUCT_QUANTITY_CHOICES = [(i, str(i)) for i in range(1, 21)]


class CartAddProductForm(forms.Form):
    quantity = forms.TypedChoiceField(choices=PRODUCT_QUANTITY_CHOICES, coerce=int)
    update = forms.BooleanField(required=False, initial=False, widget=forms.HiddenInput)

cart.py

from decimal import Decimal
from django.conf import settings
from shop.models import Product


class Cart(object):

    def __init__(self, request):
        """
        Инициализируем корзину
        """
        self.session = request.session
        cart = self.session.get(settings.CART_SESSION_ID)
        if not cart:
            # save an empty cart in the session
            cart = self.session[settings.CART_SESSION_ID] = {}
        self.cart = cart
    
    def add(self, product, quantity=1, update_quantity=False):
        """
        Добавить продукт в корзину или обновить его количество.
        """
        product_id = str(product.id)
        if product_id not in self.cart:
            self.cart[product_id] = {'quantity': 0,
                                    'price': str(product.price)}
        if update_quantity:
            self.cart[product_id]['quantity'] = quantity
        else:
            self.cart[product_id]['quantity'] += quantity
        self.save()

    def save(self):
        # Обновление сессии cart
        self.session[settings.CART_SESSION_ID] = self.cart
        # Отметить сеанс как "измененный", чтобы убедиться, что он сохранен
        self.session.modified = True
    
    def remove(self, product):
        """
        Удаление товара из корзины.
        """
        product_id = str(product.id)
        if product_id in self.cart:
            del self.cart[product_id]
            self.save()


    def __iter__(self):
        """
        Перебор элементов в корзине и получение продуктов из базы данных.
        """
        product_ids = self.cart.keys()
        # получение объектов product и добавление их в корзину
        products = Product.objects.filter(id__in=product_ids)
        for product in products:
            self.cart[str(product.id)]['product'] = product

        for item in self.cart.values():
            item['price'] = Decimal(item['price'])
            item['total_price'] = item['price'] * item['quantity']
            yield item

    def __len__(self):
        """
        Подсчет всех товаров в корзине.
        """
        return sum(item['quantity'] for item in self.cart.values())

    def get_total_price(self):
        """
        Подсчет стоимости товаров в корзине.
        """
        return sum(Decimal(item['price']) * item['quantity'] for item in
                self.cart.values())

    
    def clear(self):
        # удаление корзины из сессии
        del self.session[settings.CART_SESSION_ID]
        self.session.modified = True

The form

<form action="{% url 'cart:cart_add' product.id %}" method="post">
                    {{ cart_product_form }}
                    {% csrf_token %}
                    <button class="main-content_block-item_btn" type="submit">
                        В корзину
                    </button>
                </form>