If my system doesn’t work - I want to be alerted. If notification was supposed to be sent but wasn’t - it’s an error regardless of whether it wasn’t sent because of a bug in my code or external service being down. It may be a warning if I’m still retrying, but if I gave up - it’s an error.

“External service down, not my problem, nothing I can do” is hardly ever the case - e.g. you may need to switch to a backup provider, initiate a support call, or at least try to figure out why it’s down and for how long.