You’re using wp_count_posts( for counting posts, so it will return the number of posts.
If you want to get the number of posts for given user, you should use count_user_posts instead.
So change this line:
$count_post = wp_count_posts($post_type_name)->publish;
to:
$count_post = count_user_posts( get_current_user_id(), $post_type_name, true );
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