I tried this in my test environment I also facing the same issue, where keycloak failed to connect to the database.

After troubleshooting I got the main issue was incorrect service dependencies and connection setup b/w keycloak and mysql in docker on azure, especially when the containers start.

I have used a simple docker-compose.yml (instead of dockerfile) and setup with the official images and proper healthchecks, make sure the keycloak only starts after mysql is ready.

docker-compose.yml file like this:

version: "3.8"

services:
  mysql:
    image: mysql:8.0
    container_name: keycloak-mysql
    environment:
      MYSQL_ROOT_PASSWORD: rootpassword
      MYSQL_DATABASE: keycloak_db
      MYSQL_USER: keycloak
      MYSQL_PASSWORD: password
    healthcheck:
      test: ["CMD", "mysqladmin", "ping", "-h", "localhost"]
      interval: 5s
      timeout: 5s
      retries: 5
    ports:
      - "3306:3306"
    volumes:
      - mysql_data:/var/lib/mysql

  keycloak:
    image: bitnami/keycloak:24.0.4
    container_name: keycloak
    depends_on:
      mysql:
        condition: service_healthy
    environment:
      KEYCLOAK_DATABASE_VENDOR: mysql
      KEYCLOAK_DATABASE_HOST: mysql
      KEYCLOAK_DATABASE_PORT: 3306
      KEYCLOAK_DATABASE_NAME: keycloak_db
      KEYCLOAK_DATABASE_USER: keycloak
      KEYCLOAK_DATABASE_PASSWORD: password
      KEYCLOAK_ADMIN_USER: admin
      KEYCLOAK_ADMIN_PASSWORD: admin
    ports:
      - "8080:8080"

volumes:
  mysql_data:

Save the file and then > docker-compose up -d

the above process is working correctly it will also connect when MySQL database is ready before connecting to keycloak, i also added the health check to MySQL container the docker understand when MySQL is up and running. using the depends_on setting docker waits to start keycloak until MySQL is connections this process avoids making custom dockerfiles, if something is missing ot misconfigured it will be tricky and may cause errors. finally, by using PV for MySQL we make sure the database keeps its data even if the container restarts.

Make sure azure vm firewall and network security groups allow inbound traffic on port 8080.
Ensure docker is properly installed and running on your vm, you can view logs with docker-compose logs -f to check container startup progress