Installed WP in a subdir, can access wp-admin, but URLs are getting re-written without the subdir PATH. Where do I set this?

[aclion]

I've installed WP in a site subdir.

I can now access wp-admin pages at the expected URL.

Sort of.  I can get there manually, but my site config keeps redirecting, 
stripping URLs of the subdir path to WordPress.

My config now has

        wp-config.php
                <?php
                        define('WP_HOME',   'https://test.example.com/blog');
                        define('WP_SITEURL','https://test.example.com/blog');


and for Nginx

        location ^~ /blog {
                root /srv/www/test/wp/public;

                index index.php;
                try_files $uri $uri/ /blog/index.php?$args;

                location ~ \.php$ {
                        try_files $uri =404;
                        include fastcgi_params;
                        fastcgi_param SCRIPT_FILENAME $request_filename;
                        fastcgi_pass phpfpm;
                        fastcgi_index index.php;
                }
        }

        location / {
                root /srv/www/test/public;

                index index.php;
                try_files $uri $uri/ /index.php?$args;

                location ~ \.php {
                        try_files $uri =404;
                        include fastcgi_params;
                        fastcgi_param  SCRIPT_FILENAME 
$document_root$fastcgi_script_name;
                        fastcgi_pass phpfpm;
                        fastcgi_index index.php;
                }
        }



I visit

        https://test.example.com/blog/wp-admin/plugins.php

It displays the correct page, the "Plugins" admin page.  But the apparent URL 
(in the browser nav bar) is

        https://test.example.com/

is missing the "/blog/wp-admin/plugins.php" part of the path.

AND links in the left nav bar are too.
For example, the link for 'Pages' shows on hover

        https://test.example.com/edit.php?post_type=page

Click on it gives the expected

        404 Not Found

But a MANUAL visit to

        https://test.example.com/blog/wp-admin/edit.php?post_type=page

again gets me to the right page, with the URL displayed 'stripped' as

        https://test.example.com/?post_type=page

I need to tell 'something' -- in WP or Nginx config I guess -- to use that path.

Question is: what?

AC
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