M5-T10: add paho MQTT client with lifespan connect/reconnect and mqtt/test endpoint

app/main.py

@@ -23,6 +23,7 @@ from app.api.routes.poo import router as poo_router
 from app.api.routes.public_ip import router as public_ip_router
 from app.api.routes.ticktick import router as ticktick_router
 from app.config import get_settings
+from app.integrations.mqtt import mqtt_manager
 from app.services.auth import AuthBootstrapError, initialize_auth_schema
 from app.services.config_page import seed_missing_config_from_bootstrap, sync_app_hostname_from_bootstrap
 from app.services.public_ip import check_public_ipv4_and_notify
@@ -103,7 +104,15 @@ async def lifespan(_: FastAPI):
         coalesce=True,
     )
     scheduler.start()
+
+    # MQTT: connect if configured.
+    mqtt_manager.connect(get_settings())
+
     yield
+
+    # MQTT: clean shutdown before the process exits.
+    mqtt_manager.disconnect()
+
     scheduler.shutdown(wait=False)