When enabling push notifications on Chrome you get this warning:
The use of gcm_sender_id for authentication is discouraged and may even be removed in major Chrome updates. Which would cause the entire system to not work at all.
Roblox needs to switch to using VAPID tokens for authentication ASAP, this will also make the notification system compatible with other browsers because Chrome (and Chromium) are the only browsers that support gcm_sender_id authentication.
The push notification system right now is a ticking time bomb and will not last.
This is also the reason why enabling notifications on Edge gives this error:
DOMException: Registration failed - missing applicationServerKey.
PushManager.subscribe requires the applicationServerKey parameter for browsers like Edge.
I also have a reply here that debugs some issues with Firefox not registering service workers, and goes deeper into the technical aspects of this issue.
Credit to @tornadus11 for assisting with research.