Disable WordPress email notifications for pingbacks and trackbacks.

functions.php

<?php

// Don't send notification emails for pingbacks and trackbacks.
add_filter( 'notify_post_author', function( $maybe_notify, $comment_ID ) {
	$comment_type = get_comment_type( $comment_ID );

	if ( in_array( $comment_type, array( 'pingback', 'trackback' ), true ) ) {
		$maybe_notify = false;
	}

	return $maybe_notify;
}, 10, 2 );