<?php

namespace VendorModuleControllerIndex;

class Index extends MagentoFrameworkAppActionAction
{

    protected $resultPageFactory;

    public function __construct(
        MagentoFrameworkAppActionContext $context,
        MagentoFrameworkViewResultPageFactory $resultPageFactory)
    {
        $this->resultPageFactory = $resultPageFactory;
        parent::__construct($context);
    }

    public function execute()
    {

    }
}

use MagentoFrameworkAppActionAction;
use MagentoFrameworkAppActionContext;
use MagentoFrameworkAppResponseInterface;

class Test extends Action
{

    /**
     * @var MagentoFrameworkControllerResultJsonFactory
     */
    protected $resultJsonFactory;

    public function __construct(
        Context $context,
        MagentoFrameworkControllerResultJsonFactory $resultJsonFactory
    ) {
        parent::__construct($context);
        $this->resultJsonFactory = $resultJsonFactory;
    }

    /**
     * Dispatch request
     *
     * @return MagentoFrameworkControllerResultInterface|ResponseInterface
     * @throws MagentoFrameworkExceptionNotFoundException
     */
    public function execute()
    {
        /** @var MagentoFrameworkControllerResultJson $result */
        $result = $this->resultJsonFactory->create();
        $resultData = [
            'any_key' => 'Any data goes here',
            'success' => true,
            'time' => time(),
            'replace_button_message' => __('Your store has been already registered'),
        ];

        return $result->setData($resultData);
    }
}

<?php

namespace VendorControllerControllerIndex;

use MagentoFrameworkAppActionAction;

class Index extends Action
{
    public function execute()
    {
        $jsonResult = ['data' => 'test'];

        $this->getResponse()->representJson(
            $this->_objectManager->get(MagentoFrameworkJsonHelperData::class)->jsonEncode($jsonResult)
        );
    }
}

$this->getResponse()->representJson($this->_objectManger->get(Your Path::class)->JsonEncode($jsonResult));