how do you call Blocks in Controller Magento2?

If you want to instantiate a block you need to add to inject in the constructor an instance of \Magento\Framework\View\LayoutFactory

...
protected $layoutFactory;
...
public function __construct(
   ...
   \Magento\Framework\View\LayoutFactory $layoutFactory,
   ...
) {
   ...
   $this->layoutFactory = $layoutFactory;
   ...
}

Then you can instantiate a block like this:

$this->layoutFactory->create()->createBlock('Block\Class\Here');

if you want to access a block defined in the layout you need to inject in the constructor and instance of \Magento\Framework\View\Result\PageFactory

...
protected $resultPageFactory;
...
public function __construct(
   ...
   \Magento\Framework\View\Result\PageFactory $resultPageFactory,
   ...
) {
   ...
   $this->resultPageFactory = $resultPageFactory;
   ...
}

Then you will be able to access the block like this:

$resultPage = $this->resultPageFactory->create();
$blockInstance = $resultPage->getLayout()->getBlock('block.name.here');

1. Create the block:

    <?php
       namespace Training\Test\Block;
       class Test extends \Magento\Framework\View\Element\AbstractBlock
       {
          protected function _toHtml() {
            return "<b>Hello world from block!</b>";
          }
       }
   

2. Create an action class:

   <?php
   namespace Training\Test\Controller\Block;
   class Index extends \Magento\Framework\App\Action\Action
      {
      public function execute() {
        $layout = $this->_view->getLayout();
        $block = $layout->createBlock('Training\Test\Block\Test');
        $this->getResponse()->appendBody($block->toHtml());
      }
   }
   

See the core code:

Step 1

https://github.com/magento/magento2/blob/02e0378c33054acb0cdb8d731d1e2b2c2069bc1b/app/code/Magento/Catalog/Controller/Adminhtml/Category/Edit.php#L26-L34

public function __construct(
    \Magento\Backend\App\Action\Context $context,
    \Magento\Framework\View\Result\PageFactory $resultPageFactory,
) {
    parent::__construct($context);
    $this->resultPageFactory = $resultPageFactory;
}

Step 2

https://github.com/magento/magento2/blob/02e0378c33054acb0cdb8d731d1e2b2c2069bc1b/app/code/Magento/Catalog/Controller/Adminhtml/Category/Edit.php#L69-L70

/** @var \Magento\Backend\Model\View\Result\Page $resultPage */
$resultPage = $this->resultPageFactory->create();

Step 3

https://github.com/magento/magento2/blob/02e0378c33054acb0cdb8d731d1e2b2c2069bc1b/app/code/Magento/Catalog/Controller/Adminhtml/Category/Edit.php#L119

$block = $resultPage->getLayout()->getBlock('catalog.wysiwyg.js');