Improve block class rendering

Problem/Motivation

Currently, the custom CSS classes are injected in block's render array at the preprocess level:
https://git.drupalcode.org/project/block_class/-/blob/3.0.0/block_class....

/**
 * Implements hook_preprocess_HOOK().
 */
function block_class_preprocess_block(&$variables) {
  // Blocks coming from page manager widget does not have id.
  if (!empty($variables['elements']['#id'])) {
    $block = Block::load($variables['elements']['#id']);
    if ($block && $classes = $block->getThirdPartySetting('block_class', 'classes')) {
      $classes_array = explode(' ', $classes);
      foreach ($classes_array as $class) {
        $variables['attributes']['class'][] = Html::cleanCssIdentifier($class, []);
      }
    }
  }
}

Which requires an extra call to Block::load to load the block, to be able to access its CSS classes.

Could the Block entity be accessible at an earlier stage of the rendering flow?
This way maybe the CSS classes could be added to the render array without having to reload the block.

Steps to reproduce

Display any block with Block classes.
Another way is to run PHPUNIT Functional tests.

Proposed resolution

Look in the backtrace of the preprocess function, at earlier stages of the rendering pipeline of a Block entity, for example see:
https://git.drupalcode.org/project/drupal/-/blob/11.3.9/core/modules/blo...
\Drupal\block\BlockViewBuilder::buildPreRenderableBlock()

Maybe we could convert the current implementation with a preprocess:
block_class_preprocess_block
to a hook_block_view_alter:
block_class_block_view_alter

At the BlockViewBuilder level, the block entity object should be already available and the CSS classes could maybe be added to the build render array without having to reload the block.

Remaining tasks

User interface changes

API changes

Data model changes