Pagination & URL rewriting not working

Hello,
I have a problem with pagination on my home page when the URL rewriting is turned on. I use static page as my home page with custom template.

Here is my loop with pagination:

<?php
if ( get_query_var('paged') ) { $paged = get_query_var('paged'); }
elseif ( get_query_var('page') ) { $paged = get_query_var('page'); }
else { $paged = 1; }
query_posts('cat=1&posts_per_page=12&paged=' . $paged);
?>

<?php if ( have_posts() ) : while (have_posts()) : the_post(); ?>
<-- THE LOOP CONTENT -->
<?php endwhile; the_posts_pagination( array(
	'mid_size'  => 5,
	'prev_text' => __( '', 'textdomain' ),
	'next_text' => __( '', 'textdomain' ),
) );
else : ?>
<!-- No posts found -->
<?php endif; ?>

I have already tried to add_rewrite_rule into functions.php, which looked like this:

function plugin_name_add_rewrite_rules() {
  add_rewrite_rule('page/([0-9]+)?', 'index.php?paged=$matches[1]', 'top');
}
add_filter('init', 'plugin_name_add_rewrite_rules');

But it didn’t worked for me.

When URL rewriting is turned on and I click on the pagination’s page number (for example: mydomain.com/page/2/) the page is just reloaded and I’m still on my home page. When I paste manually address mydomain.com/?paged=2 into my browser everything is OK – I’m on the second page of pagination.

Has anyone got an idea what am I doing wrong? Please help.