Serve two locations under one domain

I have two applications that I want to serve simultaneously under one domain in nginx.

Folder structure

/var/www/phm
    /client
        /static
            /css
              main.css
          index.html
    /server
        /public
           /img
               intro.png

nginx.conf

    server_name phm.example.com;
    
    root /var/www/phm;
    index index.html index.php;
    
    location / {
        try_files $uri /client/$uri @server;
    }
    
    location @server {
        try_files /server/public/$uri /server/public/index.php$is_args$args =404;
    }
    
    location ~ .php {
        fastcgi_split_path_info ^/(.+.php)(.*)$;
        include fastcgi.conf;
        internal;
    }

My expectation is, that the following requests are answered with the according files

• phm.example.com —> /var/www/phm/client/index.html
• phm.example.com/static/css/main.css —> /var/www/phm/client/static/css/main.css
• phm.example.com/img/intro.png —> /var/www/phm/server/public/img/intro.png

server_name phm.example.com;

root /var/www/phm/client;
index index.html index.php;

location / {
    try_files $uri =404;
}

location /img {
    root /var/www/phm/server/public;

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

location ~ .php {
    fastcgi_split_path_info ^/(.+.php)(.*)$;
    include fastcgi.conf;
}