Sending Apple Push notifications to safari browsers using the HTTP/2.0 protocol - is this supported or only works for iOS

I would like to upgrade a system that currently sends out apple push notifications specifically to safari browsers. The current system uses the old binary API for communicating with APNS.

Due to payload limits in the older version I would really like to upgrade. The new API allows for more payload in the notifications. From the documentation I looked into so far, I don't quite understand if the HTTP/2.0 is also available for sending notifications to safari browsers or is it only for mobile devices?

In my case I would like to use certificate based authentication, since I already have them for the current system. Please let me know if I should still try upgrading or there is no support.