Please ensure that the Bluetooth connection between the iPhone and Xiaomi Smart Band 9 Pro is active. If disconnected, try reconnecting. If this fails, select [Forget This Device] on your Bluetooth settings and re-pair through the Mi Fitness APP, allowing all required permissions when prompted.
If Bluetooth is already connected, tap the info icon next to the connected device on the iPhone's Bluetooth settings, and make sure [Share System Notifications] is enabled. If it's not, enable it to ensure message notifications.