My WP_options db rewrite_rules Does Not Work

The rewrite is taking you back to the homepage with the Burger param but the url is being rewritten, so you aren’t seeing it.

You should be able to retrieve the value of Burger with get_query_var('Burger') which will contain the value of $matches[1]

You can read more about get_query_var in the codex

$burger = get_query_var( 'Burger');
// $burger will have the string "welldone" in it'