Nginx: How to rewrite the path to the error page?

I have an /api location that contains an HTTP authorization. I want my 401 page to be displayed on failed authorization.

Here is my file structure (If it's important, I'm running nginx on Windows)

nginx
|─html
  |
  | 401.html
  |
  |─40x_files
    |
    | script.js
    | styles.css

Here is my config

server {
    listen 80;
    server_name  example.com;
 
    error_page 401 /401.html;
    location = /401.html {
        auth_basic off;
        root html;
    }

    location /api {
        auth_basic "Restricted area";
        auth_basic_user_file ../conf/conf.d/htpasswd;
        proxy_pass   http://127.0.0.1:8080/api;
    }
}

I got two problems

1. If I just type example.com/401.html in the browser, I get an error that it cannot access files in 40x_files folder (here is filed of 401.html page)

2. If I fail the authorization, then for some reason I am redirected to this path api/40x_files/script.js, how can I return it to correct state?

I suppose I need to do some kind of rewrite, but I don’t really understand how to arrange it correctly