[hunter2_]

Sounds like that use case really wants something like silent push notifications (no sound, no toast, but it's there waiting when you decide to pull down and look for updates from all apps in one place). Yes, I said push and pull to describe a sort of hybrid model. Android offers this, but I'm not sure if desktop OSes do.

[smoldesu]

I think people would prefer notifications here, but Safari doesn't support that either.

[kitsunesoba]

Desktop Safari supports notifications, it’s only mobile Safari that lacks them.