Actually, does Chrome?
Or only internal API counts?
Looking at the docs: https://developer.chrome.com/docs/extensions/develop/concepts/service-workers/lifecycle#idle-shutdown
Events and calls to extension APIs reset these timers, and if the service worker has gone dormant, an incoming event will revive them.
MDN doesn’t mention (at least I can’t see it) what will prevent killing event page: https://developer.mozilla.org/en-US/docs/Mozilla/Add-ons/WebExtensions/Background_scripts