Last modified date in Google results

add_filter( 'generate_post_author', '__return_false' );
add_filter( 'generate_show_comments', '__return_false' );
add_filter( 'generate_post_date_output', 'tu_fancy_byline' );
function tu_fancy_byline( $date ) {
	printf( ' <span class="byline">%1$s</span>',
		sprintf( '<span class="author vcard" itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author">%4$s<a href="%1$s" title="%2$s" rel="author"><span class="author-name" itemprop="name">%3$s</span></a></span>',
			esc_url( get_author_posts_url( get_the_author_meta( 'ID' ) ) ),
			esc_attr( sprintf( __( 'View all posts by %s', 'generatepress' ), get_the_author() ) ),
			esc_html( get_the_author() ),
			get_avatar( get_the_author_meta( 'ID' ) )
		)
	);

	if ( ! is_single() && ! post_password_required() && ( comments_open() || get_comments_number() ) ) {
		echo '<span class="comments-link">';
			comments_popup_link( __( 'Leave a comment', 'generatepress' ), __( '1 Comment', 'generatepress' ), __( '% Comments', 'generatepress' ) );
		echo '</span>';
	}

	$time_string = '<time class="entry-date published" datetime="%1$s" itemprop="datePublished">%2$s</time>';
	
	if ( get_the_time( 'U' ) !== get_the_modified_time( 'U' ) ) {
		$time_string = '<time class="updated" datetime="%3$s" itemprop="dateModified">%4$s</time>';
	}
	
	$time_string = sprintf( $time_string,
		esc_attr( get_the_date( 'c' ) ),
		esc_html( get_the_date() ),
		esc_attr( get_the_modified_date( 'c' ) ),
		esc_html( get_the_modified_date() )
	);

	return sprintf( '<span class="posted-on">%s</span>', // WPCS: XSS ok, sanitization ok.
		$time_string
	);
}

As I am migrating to a new site (probably marketer starter site), I want to make sure that the above code is relevant and necessary.

1) Above code is 2 years old or more... so I want to confirm if this issue is patched in the newer themes? If not (which is absolutely okay), do I need to add the above code as it is?

2) While I was creating this ticket, I saw a lot of other threads and tickets about the same issue. Almost all had a different answer, a different solution and a different code snippet. One of most recent one was:
https://docs.generatepress.com/article/generate_post_date_show_updated_only/

I am confused... what is the correct option?

Thanks so much,
-Swadhin