How To Enable Block Editor (Gutenberg) for Existing Post Type via functions.php

Enabling the Gutenberg (block) editor for a specific post type requires these criteria:

1. The post type must be enabled in the REST API because Gutenberg uses the REST API. And for this, you need to set the show_in_rest parameter to true when registering the post type — see register_post_type().

2. The post type must support the editor, otherwise, the editor won’t appear on the post editing screen. And for this, you need to add editor to the supports parameter (which is an array) when registering the post type.

And as you already figured it, you can override (add/edit/remove) a post type’s parameters via the register_post_type_args hook. But then, you’re overriding the wrong parameter: rewrite, which doesn’t actually have the show_in_rest or supports parameter.

And I already stated the correct parameters that should be overridden/set, so here’s a working example based on your code — note that it’s a better practice to use strict comparison (e.g. === for checking equality) and in an expression (or a conditional statement), it’s recommended to put the variable on the right hand side (e.g. 'value' === $my_var and not $my_var === 'value'):

function ux_portfolio_block_editor( $args, $post_type ) {
    if ( 'featured_item' === $post_type ) {
        // 1. Enable in the REST API.
        $args['show_in_rest'] = true;

        // 2. Add the editor support.
        if ( empty( $args['supports'] ) || ! is_array( $args['supports'] ) ) {
            $args['supports'] = [ 'editor' ];
        } elseif ( ! in_array( 'editor', $args['supports'] ) ) {
            $args['supports'][] = 'editor';
        }
    }
    return $args;
}

How about (custom) taxonomies?

Well, it’s similar to post types, except that:

1. Use the register_taxonomy_args hook for overriding the taxonomy’s parameters.

2. Taxonomies do not use the supports parameter, so to enable the taxonomy (selector) in the block editor (on the post editing screen), you’d only need to set the show_in_rest parameter to true when registering the taxonomy (see register_taxonomy()) or when overriding its parameters.

So here’s an example for a taxonomy having the slug block_cat:

function ux_portfolio_block_cat_editor( $args, $taxonomy ) {
    if ( 'block_cat' === $taxonomy ) {
        $args['show_in_rest'] = true;
    }
    return $args;
}
add_filter( 'register_taxonomy_args', 'ux_portfolio_block_cat_editor', 20, 2 );