I am able to access the Metatag configuration page with the following configu...

I am able to access the Metatag configuration page with the following configuration:

Drupal-9.2.5
metatag-8.x-1.16
php7.4-fpm
nginx/1.18.0 (Ubuntu)

This doesn't look like a metatag module or Nginx config issue to me (Other configurations would have failed as well, if it was due to Nginx). I would recommend using this https://www.nginx.com/resources/wiki/start/topics/recipes/drupal/ to set Nginx with Drupal correctly.