For anyone else looking for a solution to this since there was no help from this topic https://community.hivepress.io/t/disable-listing-submitted-admin-notification-email/5776
The solution is this (add in the code snippets):
add_filter( 'hivepress/v1/emails/listing_submit', 'disable_hivepress_listing_submit', 10, 2 );
function disable_hivepress_listing_submit( $args, $email ) {
// Set the email body to an empty string to prevent it from sending
$args['body'] = '';
return $args;
}