Using a data patch to add the block into cms page

my task sounds like : "Using a data patch to add the block into cms page"

i have

1. data patch cms block

class CmcBlock implements DataPatchInterface
{
    const CMC_BLOCK = 'first_cmc_block';


    private ModuleDataSetupInterface $moduleDataSetup;


    private BlockFactory $block;

    public function __construct(
        ModuleDataSetupInterface $moduleDataSetup,
        BlockFactory $blockFactory,
    ) {
        $this->moduleDataSetup = $moduleDataSetup;
        $this->block = $blockFactory;
    }
    
    public static function getDependencies()
    {
        return [
            DependFromCmsPage::class,
        ];
    }

    public function getAliases()
    {
        return [];
    }

    public function apply()
    {
        $this->block->create()
            ->setTitle(self::CMC_BLOCK)
            ->setIdentifier(self::CMC_BLOCK)
            ->setIsActive(true)
            ->setContent($this->cmcBlockContent())
            ->setStores([Store::DEFAULT_STORE_ID])
            ->save();
    }

    public function cmcBlockContent(): string
    {
        return '<div>first CMC block content<a href="gogo">content</a></div>';
    }
}

2. data patch cms page

class CmsPage implements DataPatchInterface
{
    const CMS_PAGE = 'first_cms_page';

    /**
     * @var ModuleDataSetupInterface
     */
    private ModuleDataSetupInterface $moduleDataSetup;

    /**
     * @var PageFactory
     */
    private PageFactory $pageFactory;

    /**
     * @var PageRepositoryInterface
     */
    private PageRepositoryInterface $pageRepository;

    /**
     * @var State
     */
    private State $state;

    /**
     * @var LoggerInterface
     */
    private LoggerInterface $logger;

    public function __construct(
        ModuleDataSetupInterface $moduleDataSetup,
        PageFactory $pageFactory,
        PageRepositoryInterface $pageRepository,
        State $state,
        LoggerInterface $logger,
    ) {
        $this->moduleDataSetup = $moduleDataSetup;
        $this->pageFactory = $pageFactory;
        $this->pageRepository = $pageRepository;
        $this->state = $state;
        $this->logger = $logger;
    }

    /**
     * @return string[]
     */
    public static function getDependencies()
    {
        return[];
    }

    /**
     * @return string[]
     */
    public function getAliases()
    {
        return [];
    }

    public function apply()
    {
        try {
            $this->state->emulateAreaCode(
                Area::AREA_ADMINHTML,
                [$this, 'setupCustomCmsPage']
            );
        } catch (Exception $e) {
            $this->logger->error(
                'Error when Saving settings for patch CustomCmsPage: ' . $e->getMessage()
            );
        }

        return $this;
    }

    /**
     * This patch is to create Custom Cms Page
     */
    public function setupCustomCmsPage()
    {
        $cmsPage = $this->createPage()->setData($this->getPage());
        $this->pageRepository->save($cmsPage);
    }

    /**
     * Create page instance.
     */
    private function createPage()
    {
        return $this->pageFactory->create();
    }

    /**
     * Get Page Config
     * @return array
     */
    private function getPage(): array
    {
        return [
            'title' => 'Test CMS Page',
            'page_layout' => '1column',
            'meta_keywords' => 'test meta keywords',
            'meta_description' => 'test meta description',
            'identifier' => self::CMS_PAGE,
            'content_heading' => '',
            'content' => $this->getCmsPageHtml(),
            'layout_update_xml' => '',
            'is_active' => 1,
            'stores' => [Store::DEFAULT_STORE_ID],
            'sort_order' => 0
        ];
    }

    /**
     * Get Custom CMS page html
     * @return string
     */
    private function getCmsPageHtml(): string
    {
        return 'HTML You can set here Html Content HTML';
    }
}

how i can insert cms block to cms page pragrammatically?