WebKit team publishes guide on push notification usage to control app icon badges using Badging API.
Guides covers badge control, notification system prompt, and other technical details.
W3C: Badging API
WebKit Blog: Badging for Home Screen Web Apps
Recommendations
Developer:
Go through guide, adopt where appropriate.QA engineer:
Business as usual.PM/DM:
Adopt notification and app badges for web apps where appropriate.