The service worker can't maintain a persistent connection. Without an active tab it is shut down after 30 seconds or so. It can receive events via the Push API,

The service worker can't maintain a persistent connection. Without an active tab it is shut down after 30 seconds or so. It can receive events via the Push API, which is what you're seeing. But if you refuse notification permissions the site cannot use the Push API. I'm actually not sure how it works when you block notifications after having given permission - it's a requirement that you show a notification in response to a push, so if you're blocked, I'm not sure how the browser registers it. More broadly, I agree that it is strange you can opt into the Push API without a permission prompt. I wish it weren't the case, but I do think it would be confusing to users to request separate push and notification permissions - most consider them to be synonymous, even if they aren't.