Add a body class if the content has a cover with an specific class

theme-filters.php

/**
 * Check if the cover block has the hero class and set a global variable.
 *
 * @param string $content The block content about to be rendered.
 *
 * @return string
 */
function otk_cover_block( string $content ): string {

	// The hero is the first block in the content, so we set it once.
	global $otk_cover_block_has_hero_class;
	if ( is_null( $otk_cover_block_has_hero_class ) ) {
		$otk_cover_block_has_hero_class = (bool) preg_match( '/class="(.*?)wp-block-cover(.*?)hero(.*?)"/', $content );
	}
	return $content;

}
add_filter( 'render_block_core/cover', 'otk_cover_block' );

/**
 * Add the hero class to the body if the cover block has the hero class.
 *
 * @param array $classes The body classes.
 *
 * @return array
 */
function otk_body_class( array $classes ): array {

	global $otk_cover_block_has_hero_class;
	if ( $otk_cover_block_has_hero_class ) {
		$classes[] = 'has-hero-cover';
	}
	return $classes;

}
add_filter( 'body_class', 'otk_body_class' );