I have the following docker-compose file and when I ran docker-compose up -d --build, I got a message which indicated success. The logs did not have any exception printed.

[+] Running 2/2
 ✔ Container fastapi-tdd-docker-web-db-1  Running                                                                                                                                         0.0s
 ✔ Container fastapi-tdd-docker-web-1     Started

But when I try to access the postgres DB with docker-compose exec web-db psql -U postgres, then try c web_dev, I get this error

connection to server on socket "/var/run/postgresql/.s.PGSQL.5432" failed: FATAL:  database "web_dev" does not exist
Previous connection kept

here is my docker compose yaml file – what is going wrong here?

version: '3.8'

services:
  web:
    build: ./project
    command: uvicorn app.main:app --reload --workers 1 --host 0.0.0.0 --port 8000
    volumes:
      - ./project:/usr/src/app
    ports:
      - 8004:8000
    environment:
      - ENVIRONMENT=dev
      - TESTING=0
      - DATABASE_URL=postgres://postgres:postgres@web-db:5432/web_dev
      - DATABASE_TEST_URL=postgres://postgres:postgres@web-db:5432/web_test
    depends_on:
      - web-db

  web-db:
    build:
      context: ./project/db
      dockerfile: Dockerfile
    expose:
      - 5432
    environment:
      - POSTGRES_USER=postgres
      - POSTGRES_PASSWORD=postgres