Error for theme customize or blank page for site editor in WordPress installed in subdirectory but accessed from root

[noyle]

The background is that:

0. WordPress 6.0.2.

1. WordPress is installed in a subdirectory, e.g., ​https://www.example.com/wordpress .

2. It's accessed from root, e.g., ​https://www.example.com/. The configuration used is "Method II" on page ​https://wordpress.org/support/article/giving-wordpress-its-own-directory/ .

3. All admin pages and customized slugs can be correctly accessed from URLs via the root path.

The errors I have are:

1. If using themes 2020 or 2021, using Customize under the Appearance menu, the page will finally say "You need a higher level of permission. Sorry, you are not allowed to customize this site.".

2. If using theme 2022, using the "beta" Editor under the Appearance menu, the page is blank. When I opened F12 the developer tools screen, switched to network tab and refreshed the page, the following 3 requests are red:

   /wp-json/wp/v2/blocks?context=edit&per_page=100&_locale=user
   /wp-json/wp/v2/settings?_locale=user
   /wp-json/wp/v2/templates/twentytwentytwo//home?context=edit&_locale=user
   

   All of them were responded with the following message:

   {"code":"rest_cookie_invalid_nonce","message":"Cookie check failed","data":{"status":403}}
   

   Refer to the attachments for the above messages.

[noyle]

The message in problem 1.

[noyle]

The deveoper tools screen in problem 2.

[noyle]

Hmm, the above was done in Microsoft Edge InPrivate window. Tried again by closing the private window and reopen one for the site, all seems to be working. And they also work from other browsers now. Not sure what has really changed, weird. Will close the ticket.