How to create functional of selecting products on admin category page

I’m trying to create selecting products on category page, I make:
ui_component (category_form.xml)

    

        
            true
            Select Products
        
        
            
                
            
        
    

AddProduct class:

class AddProducts extends MagentoBackendBlockTemplate
{
    /**
     * Block template
     *
     * @var string
     */
    protected $_template = 'Vendor_Module::catalog/category/edit/grid_products.phtml';

    /**
     * @var MagentoCatalogBlockAdminhtmlCategoryTabProduct
     */
    protected $blockGrid;

    /**
     * @var MagentoFrameworkRegistry
     */
    protected $registry;

    /**
     * @var MagentoFrameworkJsonEncoderInterface
     */
    protected $jsonEncoder;

    /**
     * AssignProducts constructor.
     *
     * @param MagentoBackendBlockTemplateContext $context
     * @param MagentoFrameworkRegistry $registry
     * @param MagentoFrameworkJsonEncoderInterface $jsonEncoder
     * @param array $data
     */
    public function __construct(
        MagentoBackendBlockTemplateContext $context,
        MagentoFrameworkRegistry $registry,
        MagentoFrameworkJsonEncoderInterface $jsonEncoder,
        array $data = []
    ) {
        $this->registry = $registry;
        $this->jsonEncoder = $jsonEncoder;
        parent::__construct($context, $data);
    }

    /**
     * Retrieve instance of grid block
     *
     * @return MagentoFrameworkViewElementBlockInterface
     * @throws MagentoFrameworkExceptionLocalizedException
     */
    public function getBlockGrid()
    {
        if (null === $this->blockGrid) {
            $this->blockGrid = $this->getLayout()->createBlock(
                TabProduct::class,
                'category.product.grid'
            );
        }
        return $this->blockGrid;
    }

    /**
     * Return HTML of grid block
     *
     * @return string
     */
    public function getGridHtml()
    {
        return $this->getBlockGrid()->toHtml();
    }

    /**
     * @return string
     */
    public function getProductsJson()
    {
        $products = $this->getCategory()->getProductsPosition();
        if (!empty($products)) {
            return $this->jsonEncoder->encode($products);
        }
        return '{}';
    }

    /**
     * Retrieve current category instance
     *
     * @return array|null
     */
    public function getCategory()
    {
        return $this->registry->registry('category');
    }

class Product extends MagentoBackendBlockWidgetGridExtended
{
    /**
     * Core registry
     *
     * @var MagentoFrameworkRegistry
     */
    protected $_coreRegistry = null;

    /**
     * @var MagentoCatalogModelProductFactory
     */
    protected $_productFactory;

    /**
     * @var Status
     */
    private $status;

    /**
     * @var Visibility
     */
    private $visibility;

    /**
     * @param MagentoBackendBlockTemplateContext $context
     * @param MagentoBackendHelperData $backendHelper
     * @param MagentoCatalogModelProductFactory $productFactory
     * @param MagentoFrameworkRegistry $coreRegistry
     * @param array $data
     * @param Visibility|null $visibility
     * @param Status|null $status
     */
    public function __construct(
        MagentoBackendBlockTemplateContext $context,
        MagentoBackendHelperData $backendHelper,
        MagentoCatalogModelProductFactory $productFactory,
        MagentoFrameworkRegistry $coreRegistry,
        array $data = [],
        Visibility $visibility = null,
        Status $status = null
    ) {
        $this->_productFactory = $productFactory;
        $this->_coreRegistry = $coreRegistry;
        $this->visibility = $visibility ?: ObjectManager::getInstance()->get(Visibility::class);
        $this->status = $status ?: ObjectManager::getInstance()->get(Status::class);
        parent::__construct($context, $backendHelper, $data);
    }

    /**
     * @return void
     */
    protected function _construct()
    {
        parent::_construct();
        $this->setId('select_category_products');
        $this->setDefaultSort('entity_id');
        $this->setUseAjax(true);
    }

    /**
     * @return array|null
     */
    public function getCategory()
    {
        return $this->_coreRegistry->registry('category');
    }

    /**
     * @param Column $column
     * @return MagentoCatalogBlockAdminhtmlCategoryTabProduct
     */
    protected function _addColumnFilterToCollection($column)
    {
        // Set custom filter for in category flag
        if ($column->getId() == 'in_category') {
            $productIds = $this->_getSelectedProducts();
            if (empty($productIds)) {
                $productIds = 0;
            }
            if ($column->getFilter()->getValue()) {
                $this->getCollection()->addFieldToFilter('entity_id', ['in' => $productIds]);
            } elseif (!empty($productIds)) {
                $this->getCollection()->addFieldToFilter('entity_id', ['nin' => $productIds]);
            }
        } else {
            parent::_addColumnFilterToCollection($column);
        }
        return $this;
    }

    /**
     * @return Grid
     */
    protected function _prepareCollection()
    {
        if ($this->getCategory()->getId()) {
            $this->setDefaultFilter(['in_category' => 1]);
        }
        $collection = $this->_productFactory->create()->getCollection()->addAttributeToSelect(
            'name'
        )->addAttributeToSelect(
            'sku'
        )->addAttributeToSelect(
            'visibility'
        )->addAttributeToSelect(
            'status'
        )->addAttributeToSelect(
            'price'
        )->joinField(
            'position',
            'catalog_category_product',
            'position',
            'product_id=entity_id',
            'category_id=' . (int)$this->getRequest()->getParam('id', 0),
            'left'
        );
        $storeId = (int)$this->getRequest()->getParam('store', 0);
        if ($storeId > 0) {
            $collection->addStoreFilter($storeId);
        }
        $visible = [
            Visibility::VISIBILITY_IN_SEARCH,
            Visibility::VISIBILITY_IN_CATALOG,
            Visibility::VISIBILITY_BOTH,
        ];
        $collection->addAttributeToFilter('status', ['in' => $visible]);
        $this->setCollection($collection);

        if ($this->getCategory()->getProductsReadonly()) {
            $productIds = $this->_getSelectedProducts();
            if (empty($productIds)) {
                $productIds = 0;
            }
            $this->getCollection()->addFieldToFilter('entity_id', ['in' => $productIds]);
        }

        return parent::_prepareCollection();
    }

    /**
     * @return Extended
     */
    protected function _prepareColumns()
    {
        if (!$this->getCategory()->getProductsReadonly()) {
            $this->addColumn(
                'in_category',
                [
                    'type' => 'checkbox',
                    'name' => 'in_category',
                    'values' => $this->addSelected(),
                    'index' => 'entity_id',
                    'header_css_class' => 'col-select col-massaction',
                    'column_css_class' => 'col-select col-massaction'
                ]
            );
        }
        $this->addColumn(
            'entity_id',
            [
                'header' => __('ID'),
                'sortable' => true,
                'index' => 'entity_id',
                'header_css_class' => 'col-id',
                'column_css_class' => 'col-id'
            ]
        );
        $this->addColumn('name', ['header' => __('Name'), 'index' => 'name']);
        $this->addColumn('sku', ['header' => __('SKU'), 'index' => 'sku']);
        $this->addColumn(
            'visibility',
            [
                'header' => __('Visibility'),
                'index' => 'visibility',
                'type' => 'options',
                'options' => $this->visibility->getOptionArray(),
                'header_css_class' => 'col-visibility',
                'column_css_class' => 'col-visibility'
            ]
        );

        $this->addColumn(
            'status',
            [
                'header' => __('Status'),
                'index' => 'status',
                'type' => 'options',
                'options' => $this->status->getOptionArray()
            ]
        );

        $this->addColumn(
            'price',
            [
                'header' => __('Price'),
                'type' => 'currency',
                'currency_code' => (string)$this->_scopeConfig->getValue(
                    MagentoDirectoryModelCurrency::XML_PATH_CURRENCY_BASE,
                    MagentoStoreModelScopeInterface::SCOPE_STORE
                ),
                'index' => 'price'
            ]
        );
        $this->addColumn(
            'position',
            [
                'header' => __('Position'),
                'type' => 'number',
                'index' => 'position',
                'editable' => !$this->getCategory()->getProductsReadonly()
            ]
        );

        return parent::_prepareColumns();
    }

    /**
     * @return string
     */
    public function getGridUrl()
    {
        return $this->getUrl('catalog/*/grid', ['_current' => true]);
    }

    /**
     * @return array
     */
    protected function _getSelectedProducts()
    {
        $products = $this->getRequest()->getPost('selected_products');
        if ($products === null) {
            $products = $this->getCategory()->getProductsPosition();
            return array_keys($products);
        }
        return $products;
    }

    protected function addSelected()
    {
        //custom selected products
        return [31293];
    }
}

grid_product.phtml

< ?php

/** @var MagentoCatalogBlockAdminhtmlCategoryAssignProducts $block */

/** @var MagentoCatalogBlockAdminhtmlCategoryTabProduct $blockGrid */
$blockGrid = $block->getBlockGrid();
$gridJsObjectName = $blockGrid->getJsObjectName();
?>
< ?= $block->getGridHtml() ?>

This code I have copied from vendor of catalog category module. This code generate tab with products’ grid on category page, but when I click save button the attribute “select_products” is filled data from in_category grid but not from my grid. Could you help me, please, to find my problem.