WordPress pagination gives 404 error with custom wp_query

The category “example” has no posts. However, for user navigation and SEO purposes, this category carries a query by keyword “example”:

category.php or archive.php

$current_category = single_cat_title("", false);

$args = array(
	's' => $current_category, //search
	'posts_per_page' => 20,
	'orderby'   => 'rand'
);

$wp_query = new WP_Query( $args );

It works perfectly! The problem is pagination. It correctly displays the number of pages, but to access the page 2 appears page not found (404).

Permalink – Custom Structure:
/%category%/%postname%/

Links (examples):
https://site.com/category/example – ok! (
opens the last 20 posts and displays links to pages)

https://site.com/category/example/page/2/ – !fail! (Error 404 – Not Found)

https://site.com/category/example/?paged=2 – !fail! (Error 404 – Not Found)

Plugins or custom pagination: both fail.
Other categories with posts, or tags, search, pagination functions normally.

Research and tests that have not given results:
https://www.bamboosolutions.co.uk/fix-404-errors-wordpress-pagination/
https://stackoverflow.com/questions/22364294/pagination-on-custom-wp-query-in-wordpress-takes-to-404-error-page
https://www.ads-software.com/support/topic/custom-post-type-query_posts-pagination-404-error?replies=16
https://www.ads-software.com/support/topic/error-404-on-pagination-when-changing-posts_per_page-on-query_posts?replies=16

https://codex.www.ads-software.com/Function_Reference/paginate_links
https://codex.www.ads-software.com/Class_Reference/WP_Query#Pagination_Parameters
And all the other links, hack, plugins, scripts of the first pages of Google or WP Forum.

I appreciate any suggestions. Thank you.