Looks like someone had a similar question recently #13012 which helped me solve the above issue!

Basically, in the local env file, ensure you use localhost as the hostname

DATABASE_URL="postgresql://nest-twitter:password@localhost:5432/nest-twitter-db?schema=public"

This means when you run npx prisma studio it connects to the local postgres instance in Docker with no issues.

However, this will then break the Docker services from working together as you need to use postgres as the hostname.

So what you can do in the docker-compose.yml file is define an overriding DATABASE_URL environment variable, using postgres as the hostname

version: "3.9"
services:
  api:
    build:
      dockerfile: Dockerfile
      context: .
      # Only will build development stage from our dockerfile
      target: development
    # TBC
    volumes:
      - .:/usr/src/app
      - ./usr/src/app/node_modules
    # Run in dev Mode: npm run start:dev
    command: npm run start:dev
    depends_on: 
      - postgres
    env_file:
    - .env
    environment:
    - DATABASE_URL=postgresql://nest-twitter:password@postgres:5432/nest-twitter-db?schema=public
    ports:
      - 3000:3000
  postgres:
    image: postgres
    restart: always
    environment:
      POSTGRES_NAME: nest-twitter-db
      POSTGRES_USER: nest-twitter
      POSTGRES_PASSWORD: password
    ports: 
      - '5432:5432'
    volumes:
      - nest-twitter-db:/var/lib/postgresql/data

volumes:
  nest-twitter-db:

# Run Prisma migrations.
RUN npx prisma migrate dev --name init

it doesn't make sense to run migrations at docker image build time. The migrations should be run within the entrypoint of the image, not when its being built.

Then when the container is deployed, the migrations run before the application is started in each environment in which it's deployed.