Setup Adminer, Postgres and Traefik on a single VPS

I am not quite sure how to setup networks in docker-compose.yml for Postgres and Adminer. All examples I can find are about Postgres and Adminer in same docker-compose.yml meaning separate Adminer for each app, and I dont want that, I want single Adminer for entire VPS instance.

I have another docker-compose.yml with Traefik and Portainer, and I want to add Adminer in that file but I am not sure how to set up networks.

I am aware that with Adminer I can connect to any database with IP, but since this is same VPS I guess Adminer can read hostname trough Docker network.

I have proxy external network that Traefik uses to discover containers. I assume I can’t have Adminer and Postgres on same internal network since they aren’t defined in same container.

Note that I need Postgres to be available for connections from external servers as I will use it’s connection string in Github actions for building the app container, Next.js app needs to read data to prerender pages.

Do you have advice or example how to setup networks? Here is my incomplete setup so far:

docker-compose.yml for reverse proxy in which I want to add Adminer

services:
  traefik:
	image: "traefik:v2.5.6"
	networks:
	  - proxy
  ...

  adminer:
	image: adminer:4.8.1-standalone
	networks:
	  - proxy
	labels:
	  - "traefik.http.routers.adminer.rule=Host(`adminer.${DOMAIN}`)"
	  - "traefik.http.services.adminer.loadbalancer.server.port=8080"

networks:
  proxy:
	external: true

docker-compose.yml for my app, Adminer should connect to this Postgres container

 app:
	depends_on:
	  - postgres-db-prod
  ...
	networks:
	  - proxy
	  - internal

  postgres-db-prod:
	image: postgres:14-alpine
	container_name: postgres-db-prod
	restart: unless-stopped
	ports:
	  - 5432:5432
	volumes:
	  - ./prisma/pg-data:/var/lib/postgresql/data
	env_file:
	  - .env.local
	labels:
	  - 'traefik.enable=false'
	networks:
	  - proxy
	  - internal

networks:
  proxy:
	external: true
  internal:
	external: false