How to Have a Pure HTML Sub Directory In WP Site

It can be achieved by either of the two ways:

Way #1

Create a WordPress page template first in your WordPress theme (or child theme). Suppose the name of the file is: my-app.php, and the content is:

<?php
/**
 * Template name: My App Page
 */

echo "Here's what I want to show";

Now, create a WordPress page from Pages. Make the page slug to app.
slug 'app'

Select the “My App Page” template from the right meta box’s “Templates”.
Page Template

Save the page, and you can access the page using example.com/app/. What you want to show in that page, place all of them in the Page Template file.

The page template method is helpful regardless whether your your page content is tied with WordPress or not.

More details on Page Templates – Developer Resources

Way #2

Create your app/ folder in WordPress root, where folders like wp-admin, wp-content, and wp-includes resides.

Make your index.html or index.php file there, with respective contents.

Access the folder using example.com/app/. You are done! 🙂
/app directly

But I cannot assure whether the folder stays or not after WordPress updates. I never tried.