The Android app "Home Assistant" offers besides numerous cell phone sensor values in Home Assistant also a very simple way to receive notifications from Home Assistant:https://play.google.com/store/apps/details?id=io.homeassistant.companion.android&hl=de_AT&gl=US.

Alternatively, the messenger Signal can be used for notifications, see: Send Signal messages via API: signal-cli-rest-api.

Anyone who has published Home Assistant on the internet via https can also use the HTML5 Push Notifications integration:

This allows a notification to be activated in the browser: without any additional app, purely through the browser.

Those who install the Home Assistant app will notice that Home Assistant regularly announces updating the phone sensors after Home Assistant:

Refresh Sensors.

By default, a notification with "Update sensors" is displayed every 15 minutes:

The notice can be easily removed by long pressing on the notification and disabling "SensorWorker":

Deactivating the SensorWorker does not affect the notifications stored in the automations, they still remain active. To receive a notification when an event occurs, an automation can be created for this purpose by clicking on "Configuration" and "Automation":

Notification when a certain value is reached

As an example, I created a notification for monitoring the humidity:

I created a new automation for this notification in Configuration / Automation:

The notification can be tested later with "RUN ACTIONS", but first to the settings of this automation:

service: notify.mobile_app_sm_a405fn
data:
  title: Luftfeuchtigkeit Bad
  message: >-
    Luftfeuchtigkeit: {{states('sensor.bad_2')}}%
    Temperatur:{{states('sensor.bad')}}°C