Update the block content with elements class names.

function wp_render_elements_support( $block_content, $block ) {
	if ( ! $block_content ) {
		return $block_content;
	}

	$block_type                    = WP_Block_Type_Registry::get_instance()->get_registered( $block['blockName'] );
	$skip_link_color_serialization = wp_should_skip_block_supports_serialization( $block_type, 'color', 'link' );

	if ( $skip_link_color_serialization ) {
		return $block_content;
	}

	$link_color = null;
	if ( ! empty( $block['attrs'] ) ) {
		$link_color = _wp_array_get( $block['attrs'], array( 'style', 'elements', 'link', 'color', 'text' ), null );
	}

	/*
	 * For now we only care about link color.
	 * This code in the future when we have a public API
	 * should take advantage of WP_Theme_JSON::compute_style_properties
	 * and work for any element and style.
	 */
	if ( null === $link_color ) {
		return $block_content;
	}

	$class_name = wp_get_elements_class_name( $block );

	// Like the layout hook this assumes the hook only applies to blocks with a single wrapper.
	// Retrieve the opening tag of the first HTML element.
	$html_element_matches = array();
	preg_match( '/]+>/', $block_content, $html_element_matches, PREG_OFFSET_CAPTURE );
	$first_element = $html_element_matches[0][0];
	// If the first HTML element has a class attribute just add the new class
	// as we do on layout and duotone.
	if ( strpos( $first_element, 'class="' ) !== false ) {
		$content = preg_replace(
			'/' . preg_quote( 'class="', '/' ) . '/',
			'class="' . $class_name . ' ',
			$block_content,
			1
		);
	} else {
		// If the first HTML element has no class attribute we should inject the attribute before the attribute at the end.
		$first_element_offset = $html_element_matches[0][1];
		$content              = substr_replace( $block_content, ' class="' . $class_name . '"', $first_element_offset + strlen( $first_element ) - 1, 0 );
	}

	return $content;
}