Add FastAPI hello-world structure with Docker and DB health check

- app/main.py: root endpoint + /health that reports DB connectivity
- app/db.py: pymysql connection check from MYSQL_* env vars, logged at startup
- Dockerfile: python:3.12-slim, port 8720
- docker-compose.yml: mysql:8.2 with healthcheck, app waits for DB ready
- requirements.txt: fastapi, uvicorn, pymysql

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

app/db.py

@@ -0,0 +1,22 @@
+import os
+import pymysql
+
+
+def _params() -> dict:
+    return {
+        "host": os.environ["MYSQL_HOST"],
+        "port": int(os.environ.get("MYSQL_PORT", 3306)),
+        "user": os.environ["MYSQL_USER"],
+        "password": os.environ["MYSQL_PASSWORD"],
+        "database": os.environ["MYSQL_DATABASE"],
+        "connect_timeout": 3,
+    }
+
+
+def check_db() -> bool:
+    try:
+        conn = pymysql.connect(**_params())
+        conn.close()
+        return True
+    except Exception:
+        return False