How do I rewrite URL that has custom parameter

You can use a rewrite endpoint for this.

The first step is to give your custom taxonomy an endpoint mask when you register the taxonomy:

$args = [
    'rewrite' => [
        'slug' => 'topic',
        'ep_mask' => EP_CATEGORIES
    ],
    // the rest of your args...
];
register_taxonomy( 'topic', array( 'post' ), $args );

The next step is to add the endpoint. This should be hooked to run on init, just like your taxonomy registration code.

add_rewrite_endpoint( 'type', EP_CATEGORIES );

Don’t forget to flush rewrite rules after adding this code. The easiest way to do this is by visiting the Settings > Permalinks page.

You should now be able to add type/newsletter onto the end of your taxonomy links. To access the passed value, use get_query_var:

$type = get_query_var( 'type', false );

If the code currently expects to find type in $_GET['type'] and you can’t change that, you can manually set that value before the code that tries to access it:

$_GET['type'] = get_query_var( 'type', false );

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