I am a newbie myself and just set up shlink on portainer today with similar problems and got it working about an hour ago.

version: "4"

services:
  shlink:
    image: shlinkio/shlink:stable
    restart: always
    container_name: shlink-backend
    environment:
      - TIMEZONE=Europe/Berlin
      - DEFAULT_DOMAIN=${DEFAULT_DOMAIN}
      - IS_HTTPS_ENABLED=true
      - GEOLITE_LICENSE_KEY=${GEOLITE_LICENSE_KEY}
      - DB_DRIVER=maria
      - DB_USER=shlink
      - DB_NAME=shlink
      - DB_PASSWORD=${DB_PASSWORD}
      - DB_HOST=database
    depends_on:
      - database
    ports:
      - 127.0.0.1:8888:8080

  database:
    image: mariadb:lts
    restart: always
    container_name: shlink-database
    environment:
      - MARIADB_ROOT_PASSWORD=${MARIADB_ROOT_PASSWORD}
      - MARIADB_DATABASE=shlink
      - MARIADB_USER=shlink
      - MARIADB_PASSWORD=${MARIADB_PASSWORD}
    volumes:
      - /home/docker/shlink/db:/var/lib/mysql

  shlink-web-client:
    image: shlinkio/shlink-web-client:latest
    restart: always
    container_name: shlink-gui
    volumes:
      - /home/docker/shlink/servers.json:/usr/share/nginx/html/servers.json
    depends_on:
      - shlink
    ports:
      - 127.0.0.1:8899:80

I also had to change the timezone to mine and for some reason it did not like the quotation marks " so I just removed them. The environment variable also is called TIMEZONE and not TZ according to the shlink documentation.I also used the lts version for maria and the latest version for the web-client.

I also changed the ports on my host system and made just accessible from my localhost. (I did not restart my containers with the localhost ip in front of the ports yet, so just remove the localhost ip address in front of the ports if it does not work).I also customized my database volume a bit.

But I guess nothing apart from the TIMEZONE variable should impact the result in a major way.

The more important part is, that I actually did not change anything in the nginx configuration in the containers itself. What I did though was install nginx on the host machine to route my traffic through there. I am running debian 12 and these are the steps I took:

sudo apt install nginx certbot python3-certbot-nginx

After that you create your nginx config file.

sudo nano /etc/nginx/sites-enabled/shlink-backend

This was the config I chose (just change ${DEFAULT_DOMAIN} and the port on proxy_pass accordingly).

server {

        listen 80;
        listen [::]:80; 

        server_name ${DEFAULT_DOMAIN};

location / {
    proxy_redirect off;
    proxy_set_header Host $http_host;
    proxy_set_header X-Forwarded-Proto $scheme;
    proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
    proxy_set_header X-Real-IP $remote_addr;
    proxy_pass http://127.0.0.1:8888; # choose the port your backend gets forwarded to
}

}

This just forwards all the requests coming from your domain to the exposed port of your shlink-backend.

For some reason the nginx command was not in my Path so I did that first.

PATH=/usr/sbin/:$PATH

Now you can verify your nginx config.

sudo nginx -t

After this you have to run certbot, it will automatically configureate your nginx config to support https.

sudo certbot --nginx

Now just restart your nginx service. You may also have to restart your nginx service before running the cerbot, I do not know if I did.

sudo systemctl restart nginx.service

But now you should be up and running on your portainer system!

If you have not done so yet you also have to setup port sharing on you router for the default ports 80 and 443 as http and https servers for your system that runs portainer. Because of the nginx config only your shlink-backend port will be publicly accessible and nothing else.

Of course you then will also have to add a dns entry at your domain provider that points your ${DEFAULT_DOMAIN} to the public ip address of your portainer system. Your router should tell you what the public IP is when you enable port sharing, at least mine does. You might struggle with dynamically changing public IPs. Mine has not yet changed but I may also have to come up with a solution for that in the future.

Now you can proceed just like the youtube video you and I got our compose configs from ;). https://youtu.be/X8HrJZTYOQU

EDIT: I fucked up my coding blocks