Websites can ask you to accept several different kinds of communications and updates:

• Desktop notifications - if allowed, the site can send notifications for Firefox to display in the lower corner of your screen until you close the last tab for a site.

• Web push notifications - if allowed, the site can send desktop notifications for Firefox to display in the lower corner of your screen even after the last tab for the site is closed (until you exit Firefox).

• Web push updates - if allowed, the site can send Firefox updates in the background, which presumably is more efficient that forcibly refreshing a page or having a script in the page keep checking for updates. This push feature is NOT a desktop notification, but Firefox may use the notification permission panel, which I hope will be changed in the future since that's a bit confusing.

[...]

All-Site Persistent Disable

There are two different preferences for notifications, a master switch, and one which is specific to background (web push) notifications that can appear after you leave the site which sends them.

(1) In a new tab, type or paste about:config in the address bar and press Enter/Return. Click the button promising to be careful.

(2) In the search box above the list, type or paste webno and pause while the list is filtered

(3) To disable PUSH NOTIFICATIONS, double-click the dom.webnotifications.serviceworker.enabled preference to switch its value from true to false -- sites can still generate desktop notifications while you have a tab open to the site

(4) To disable ALL NOTIFICATIONS, double-click the dom.webnotifications.enabled preference to switch its value from true to false -- this is a master switch, you won't get any desktop notifications from sites

(5) To also disable BACKGROUND UPDATES, double-click the dom.push.enabled preference to switch its value from true to false -- but that may block actually useful services from sites you trust, so I don't recommend it at this point.