Please follow [the guide][1] how to install Drupal 10

`composer create-project drupal/recommended-project my_site_name_dir`

You need to keep this structure, the "project-root" will be at `my_site_name_dir` and your webserver must point to the "web-root" which will be at `my_site_name_dir/web` by default, AFAIS you want to change only the directory of the web-root which you can easily do by adjusting the composer.json drupal-scaffold, e.g 

```
"extra": {
        "drupal-scaffold": {
            "locations": {
                "web-root": "web/"
            }
        },
```
and adjust the installer_paths accordingly

and make composer install


  [1]: https://www.drupal.org/docs/getting-started/installing-drupal/get-the-code