Show only the updated date if set

gistfile1.txt

add_filter( 'generate_post_date_output', function( $output, $time_string ) {
	$time_string = '<time class="entry-date published" datetime="%1$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
	);
}, 10, 2 );