I was reading about this somewhere but I can’t remember where…
And I can’t find bugzilla issue for it either.
The MDN says they are NOT persistent across browser sessions: https://developer.mozilla.org/en-US/docs/Mozilla/Add-ons/WebExtensions/API/alarms
But in Chrome they are, although their docs doesn’t say it: https://developer.chrome.com/docs/extensions/reference/alarms/