Hide custom post type and use its slug in new plugin menu

You’re passing edit.php?post_type=reserve as first parameter and that should be parent menu slug. Instead pass it as menu_slug parameter, see code snippet below.

add_submenu_page( 
    'reserve/admin', 
    'Reserve',
    'Reserve Builder', 
    'view_reservation_plugin', // $capability
    'edit.php?post_type=reserve' 
);