According to wikipedia article on status codes, Nginx has a custom error code when http traffic is sent to https port(error code 497)

And according to nginx docs on error_page, you can define a URI that will be shown for a specific error.
Thus we can create a uri that clients will be sent to when error code 497 is raised.

nginx.conf

#lets assume your IP address is 89.89.89.89 and also that you want nginx to listen on port 7000 and your app is running on port 3000

server {
    listen 7000 ssl;
 
    ssl_certificate /path/to/ssl_certificate.cer;
    ssl_certificate_key /path/to/ssl_certificate_key.key;
    ssl_client_certificate /path/to/ssl_client_certificate.cer;

    error_page 497 301 =307 https://89.89.89.89:7000$request_uri;

    location / {
        proxy_pass http://89.89.89.89:3000/;

        proxy_pass_header Server;
        proxy_set_header Host $http_host;
        proxy_redirect off;
        proxy_set_header X-Real-IP $remote_addr;
        proxy_set_header X-Forwarded-Protocol $scheme;
    }
}

However if a client makes a request via any other method except a GET, that request will be turned into a GET. Thus to preserve the request method that the client came in via; we use error processing redirects as shown in nginx docs on error_page

And thats why we use the 301 =307 redirect.

Using the nginx.conf file shown here, we are able to have http and https listen in on the same port

One port to rule them all, shows someone has atleast implemented it in the java world.

Have you ever deployed such a solution in a production environment?

I have not -- nor would I ever recommend it be done. As a consultant I try to encourage my clients to use standardized and proven technologies. No system seems to properly implement those RFC's except for edge cases -- and that would not be something I would want to suggest or support.