get_query_var(‘paged’) for WP_Comment_Query always return 1 when using paginate_comments_links()

I’m sure the problem is in this line of code, since it ALWAYS return
1:

$paged = (get_query_var('paged')) ? get_query_var('paged') : 1;

Yes, that’s correct.

And to retrieve the page number of the current comments page, where the URL contains the /comment-page-<number>, use get_query_var( 'cpage' ) and not get_query_var( 'paged' ), i.e. the query var name is cpage and not paged.