带有 PHP 的子目录的 Nginx 配置返回 404

我有一个网站 www.example.com 使用自定义 PHP 框架和加载完全不同框架的 CMS。它最初是在 apache2 上，现在我正在尝试转移到 nginx。www 域加载文件，但在加载子目录中的代码库时，它只是在我的 nginx 上返回 404。如果我切换回 apache2，它可以正常加载。这是我的配置，我基本上是通过查看其他 stackoverflow 答案拼凑出来的：

server {
listen 80 default;
client_max_body_size 256M;
access_log /var/log/nginx/site.access.log;

root /site;
index index.php;

if (!-e $request_filename) {
    rewrite ^.*$ /index.php last;
}

location ~ \.php$ {
    fastcgi_pass php-fpm:9000;
    fastcgi_index index.php;
    fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
    fastcgi_param PHP_VALUE "error_log=/var/log/nginx/site_php_errors.log";
    fastcgi_buffers 32 32k;
    fastcgi_buffer_size 64k;
    include fastcgi_params;
}

location /cms {
    root /cms/;
}

location ~ /cms/.+\.php$ {
    fastcgi_pass php-fpm:9000;
    fastcgi_index index.php;
    fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
    fastcgi_param PHP_VALUE "error_log=/var/log/nginx/site_php_errors.log";
    fastcgi_buffers 32 32k;
    fastcgi_buffer_size 64k;
    include fastcgi_params;
}

}

我试过这个答案，但运气不佳。我必须错误地设置了一些基本配置，但似乎无法弄清楚是哪个。/cms中的.htaccess如下：

RewriteEngine On
RewriteBase /cms

RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ index.php?request=$1 [L,QSA]

编辑：使用此示例更新了配置，我现在可以登录到 CMS，但它立即进入 302 重定向循环，我无法弄清楚为什么会发生这种情况：

server {
listen 80 default_server;

# client_max_body_size 256M;

root /application;

index index.php;

server_name _;

# access_log /var/log/nginx/application.access.log;

location / {
   try_files $uri $uri/ /index.php$is_args$args;
}

location /cms {
        alias /application/cms;
        try_files $uri $uri/ @cms;

        location ~ \.php$ {
            include fastcgi_params;
            fastcgi_param SCRIPT_FILENAME $request_filename;
            fastcgi_pass php-fpm:9000;
        }
    }

location @cms {
    rewrite /cms/(.*)$ /cms/index.php?/$1 last;
}

location ~ \.php$ {
    include fastcgi_params;
    fastcgi_pass php-fpm:9000;
    fastcgi_index index.php;
    fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
    fastcgi_param PHP_VALUE "error_log=/var/log/nginx/application_php_errors.log";
    fastcgi_buffers 32 32k;
    fastcgi_buffer_size 64k;
}

}