That tutorial seems to be regards what comes to mind when I think of Push Notification (i.e. a notification shown even if application is not running, pushed over the internet from a server)
For Linux it looks like (with a choice of 2 dependencies) local notifications (as provided in the WinToast you linked to) are also pretty straightfoward as well : Desktop notifications - ArchWiki
After reading the juce::PushNotification docs, to me it looks like the intention is to support both toast and push notifications (not sure why the language/terminology used in the docs are like this, but anyways):
Both remote and local notifications are supported.