How to Purge All Categories at the Same Time?

no , it won’t work with * like that

there is no direct way to do this , you need to create a php file , put it at same dir as your wp-config.php , with code:

<?php
require( './wp-load.php' );
if ( defined('LSCWP_V')) {
do_action( 'litespeed_purge', 'tax' );
do_action( 'litespeed_purge', 'category' );
}

access by browser , it will purge all category pages