Ports are normally exposed within the docker-compose file (see below). The Airflow UI is accessible through SSH and execution is also successul if triggered from there. Here's the content of my docker-compose file.

services:
  postgres:
    image: postgres:13
    environment:
      - POSTGRES_USER=airflow
      - POSTGRES_PASSWORD=airflow
      - POSTGRES_DB=airflow
    ports:
      - "5434:5432"
  init_db:
    build:
      context: .
      dockerfile: Dockerfile
    command: bash -c "airflow db init && airflow db upgrade"
    env_file: .env
    depends_on:
      - postgres
  scheduler:
    build:
      context: .
      dockerfile: Dockerfile
    restart: on-failure
    command:  bash -c "airflow scheduler"
    env_file: .env
    depends_on:
      - postgres
    ports:
      - "8080:8793"
    volumes:
      - ./airflow_dags:/opt/airflow/dags
      - ./airflow_logs:/opt/airflow/logs
    healthcheck:
      test: ["CMD-SHELL", "[ -f /usr/local/airflow/airflow-webserver.pid ]"]
      interval: 30s
      timeout: 30s
      retries: 3
  webserver:
    build:
      context: .
      dockerfile: Dockerfile
    hostname: webserver
    restart: always
    env_file: .env
    depends_on:
      - postgres
    command: bash -c "airflow users create -r Admin -u admin -e admin@example.com -f admin -l user -p admin && airflow webserver"
    volumes:
      - ./airflow_dags:/opt/airflow/dags
      - ./airflow_logs:/opt/airflow/logs
    ports:
      - "5000:8080"
    healthcheck:
      test: ["CMD-SHELL", "[ -f /usr/local/airflow/airflow-webserver.pid ]"]
      interval: 30s
      timeout: 30s
      retries: 32