Yes, this is quite nice.
Apple finally decided to play along.
Web Push notifications were implemented in HABot Walkthrough (7/n): Push Notifications back in 2018 (!).
But now that they are universal it might be time to revisit them. For instance they allow your local instance to push notifications securely to your phone, tablet or desktop, without an intermediate service like openHAB Cloud involved. When visiting the main UI you would have an option to receive notifications (like many websites annoyingly try to offer) but if you accept you’ll be notified on your phone or desktop even if you don’t have the UI opened.