How to force nginx to give a separate folder for domain.com/sub?

Question

Nginx

We have a project in Laravel.
And it took a part of requests for / sub to be processed by a separate script. But bad luck, a separate script is also written in Laravel and is essentially an independent project.
I just can't get my brain to figure out how to change the nginx config to make everything work. Help to understand, please.
Now the config is standard like everyone else:

server {
# все как у всех
   listen 80 default_server;
   server_name domain.cm;
   root /home/domain.com/public;
   index index.php;

# тут все стандартно 
    location / {
        try_files $uri $uri/ /index.php?$query_string;
    }

# и тут все стандартно 
   location ~ \.php$ {
       fastcgi_pass 127.0.0.1:9001;
       fastcgi_index index.php;
       fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
       include fastcgi_params;
   }
}

Accordingly, /home/domain.com is the project. And /home/domain.com/public is the entry point to the application.
And so in /home/domain.com/sub there is a subproject. And its entry point is naturally /home/domain.com/sub/public
And you need to give it as domain.com/sub. And so that the user does not redirect to domain.com/sub/public
I tried to implement what I need like this:

location /sub {
         alias /home/domain.com/sub/public/;
         try_files $uri $uri/ /index.php?$query_string;
 }

Does not work.
Tried like this:

location /sub {
       root /home/domain.com/sub/public/;
       rewrite ^(.*) /index.php$1;
  }

Doesn't matter.
I feel that the solution is simple and should be on the surface. Well, it's like a thorn in my head. When you know a word, but you can't remember.

Answer 1

proxy_pass?

Answer 2

It's funny. The same question came up again. It’s useful to ask a question, but it turns out that everything is already there. For over a year now. And the situation is one on one. Only in a different place with different people and a different project.
I don’t know if the question will rise from the comment to the top in the search results. But it's as relevant as ever.