Answer
A full restart of the server infrastructure has resolved this exact persistent per-user missing-notification-badge symptom, even though there's no visible configuration setting specifically for the notification badge itself to check beforehand. Separately, if many users are getting flooded with excessive or seemingly miscellaneous Streams alerts rather than one specific user missing their own badge, check for overly broad Custom Events tied to routine, high-volume actions, for example Purchase Order or Purchase Order Requisition line creation, that are firing notices far more broadly than intended. Disabling or narrowing the scope of those specific overly-broad events stops the flood and lets genuinely relevant notifications display correctly for everyone again.