Use nginx as reverse proxy for all Docker containers

I'm running Docker on my Raspberry Pi 4 with some containerized web apps and I want all traffic to go through nginx as reverse proxy.

My problem is that I can access the Docker container ports from any device in my network, i. e. I'm bypassing nginx.

This is my nginx config:

server {
    listen 80;
    server_name myRaspi;

    location /cool {
        proxy_pass         http://127.0.0.1:5000/cool;
        proxy_http_version 1.1;
        proxy_set_header   Upgrade $http_upgrade;
        proxy_set_header   Connection keep-alive;
        proxy_set_header   Connection "Upgrade";
        proxy_set_header   Host $host;
        proxy_cache_bypass $http_upgrade;
        proxy_set_header   X-Forwarded-For $proxy_add_x_forwarded_for;
        proxy_set_header   X-Forwarded-Proto $scheme;
    }
}

As you can see, I'm forwarding the traffic for http://myRaspi/cool to http://localhost:5000/cool (a web app running inside a Docker container). At the moment, I can access both http://myRaspi/cool and http://myRaspi:5000/cool from any device in my network.

I followed the official Docker docs and configured the following:

iptables -I DOCKER-USER -i ext_if ! -s 192.168.174.0/24 -j DROP

Executing sudo iptables --list shows the new rule.
Since all of my network devices are in the subnet 192.168.175, so I'd expect that now all traffic to both http://myRaspi/cool and http://myRaspi:5000/cool should not work (as I'm blocking everything except 192.168.174, but I'm in 192.168.175).
Unfortunately, this does not work: I can still access both http://myRaspi/cool and http://myRaspi:5000/cool.

After sudo reboot, the formerly created rule is gone and sudo iptables --list doesn't contain it anymore.

Since I'm still a novice to the Docker/Linux/nginx network world, I'd appreciate your help on how to configure Docker/nginx so that all traffic goes through nginx as reverse proxy and access to container ports from outside this Raspi is not possible.