Nginx redirect to another domain without trailing uri

I am trying to get http://foo.mydomain.xyz/one/two/three.json by calling http://bar.mydomain.xyz/cat/one/two/three.json. I am using the following configuration:

server {
        listen 80;
        listen [::]:80;
        server_name bar.mydomain.xyz;
        absolute_redirect off;

        location / {
          proxy_pass http://localhost:8080;
        }

        location /cat {
          rewrite ^(/cat) http://foo.mydomain.xyz$request_uri permanent;
        }
}
server {
        listen 80;
        listen [::]:80;
        server_name foo.mydomain.xyz;

        location / {
          proxy_pass http://localhost:7070;
        }
}

Using this configuration when I am calling: http://bar.mydomain.xyz/cat/ it is redirecting me to http://foo.mydomain.xyz/ successfully. But when I am calling http://bar.mydomain.xyz/cat/one/two/three.json it is returning http://foo.mydomain.xyz/cat/one/two/three.json. Notice the /cat is not removing from the url. How can I solve this?

Another approach is to capture the part in the location directive:

location / {
    proxy_pass http://localhost:8080;
}

location ~ ^/cat(/.+)$ {
    return 301 http://foo.example.com$1$is_args$args;
}