chore(prod): startup migrations, readiness checks and backend healthcheck

- add backend entrypoint that can run alembic upgrade head on startup
- add RUN_MIGRATIONS_ON_STARTUP setting and compose wiring
- add /health/live and /health/ready endpoints with db+redis checks
- add backend container healthcheck against readiness endpoint
- document readiness and startup migration behavior

app/main.py

@@ -1,6 +1,7 @@
 from contextlib import asynccontextmanager
 
-from fastapi import FastAPI
+from fastapi import FastAPI, HTTPException, status
+from sqlalchemy import text
 
 from app.auth.router import router as auth_router
 from app.chats.router import router as chats_router
@@ -14,7 +15,7 @@ from app.notifications.router import router as notifications_router
 from app.realtime.router import router as realtime_router
 from app.realtime.service import realtime_gateway
 from app.users.router import router as users_router
-from app.utils.redis_client import close_redis_client
+from app.utils.redis_client import close_redis_client, get_redis_client
 
 
 @asynccontextmanager
@@ -36,6 +37,36 @@ async def health() -> dict[str, str]:
     return {"status": "ok"}
 
 
+@app.get("/health/live", tags=["health"])
+async def health_live() -> dict[str, str]:
+    return {"status": "ok"}
+
+
+@app.get("/health/ready", tags=["health"])
+async def health_ready() -> dict[str, str]:
+    db_ok = False
+    redis_ok = False
+    try:
+        async with engine.connect() as conn:
+            await conn.execute(text("SELECT 1"))
+        db_ok = True
+    except Exception:
+        db_ok = False
+    try:
+        redis = get_redis_client()
+        pong = await redis.ping()
+        redis_ok = bool(pong)
+    except Exception:
+        redis_ok = False
+
+    if not db_ok or not redis_ok:
+        raise HTTPException(
+            status_code=status.HTTP_503_SERVICE_UNAVAILABLE,
+            detail={"status": "not_ready", "db": db_ok, "redis": redis_ok},
+        )
+    return {"status": "ready", "db": "ok", "redis": "ok"}
+
+
 app.include_router(auth_router, prefix=settings.api_v1_prefix)
 app.include_router(users_router, prefix=settings.api_v1_prefix)
 app.include_router(chats_router, prefix=settings.api_v1_prefix)