How to make an ajax request in Magento 2.4?

Question

Magento

It is necessary to execute an ajax request from the product page. The Internet is full of examples of how to do this for older versions of Magento, there are options from my custom page, I try by analogy, it doesn’t work - if through the address bar of the browser - everything works, if from javascript - no. The controller's constructor fires, but the execute() method is not called, ajax itself returns with a 302 status, after which the product page is called again

$.ajax({
                        url: baseUrl + 'module/ajax/fooaction',
                        type: "POST",
                        data: {},
                        showLoader: true,
                        cache: false,
                        crossDomain:true,
                        dataType: 'json',
                        success: function(response){
                        }
                    });

The controller code is something like this

<?php
namespace Vendor\Module\Controller\Ajax;

use Magento\Framework\App\Action\Context;
use Magento\Framework\Controller\Result\JsonFactory;
use Magento\Framework\App\Action\HttpGetActionInterface;

class FooAction implements HttpGetActionInterface
{
    /**
     * @var \Magento\Framework\App\Action\Contex
     */
    private $context;
    /**
     * @var \Magento\Framework\Controller\Result\JsonFactory
     */
    protected $resultJsonFactory;

    /**
     * @param \Magento\Framework\App\Action\Context $context
     * @param \Magento\Framework\Controller\Result\JsonFactory $resultJsonFactory
     */
    public function __construct(Context $context, JsonFactory $resultJsonFactory)
    {
        $this->context = $context;
        $this->resultJsonFactory = $resultJsonFactory;
    }

    /**
     * @return json
     */
    public function execute()
    {
        $params = $this->context->getRequest()->getParams();     
        $resultJson = $this->resultJsonFactory->create();
        $resultJson->setData(['message' => 'Hello world', 'success' => true]);
        return $resultJson;
    }
}

Why approximately, because this is already its 10-20 iteration, I tried different options, right now this is:

...............
use Magento\Framework\App\Action\HttpPostActionInterface;
use Magento\Framework\App\Action\HttpGetActionInterface;
use Magento\Framework\App\Action\Action;

class FooAction extends Action implements HttpGetActionInterface, HttpPostActionInterface
{
    /**
     * @var \Magento\Framework\App\Action\Contex
     */
    private $context;
    /**
     * @var \Magento\Framework\Controller\Result\JsonFactory
     */
    protected $resultJsonFactory;

    /**
     * @param \Magento\Framework\App\Action\Context $context
     * @param \Magento\Framework\Controller\Result\JsonFactory $resultJsonFactory
     */
    public function __construct(Context $context, JsonFactory $resultJsonFactory)
    {
        $this->context = $context;
        $this->resultJsonFactory = $resultJsonFactory;
        parent::__construct($context);
    }
............................................................

routes.xml

<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:App/etc/routes.xsd">
    <router id="standard">
        <route id="module" frontName="module">
            <module name="Vendor_module" />
        </route>
    </router>
</config>

What am I doing wrong?