Most status page products integrate to monitoring tools like Datadog[1], large teams like github would have it automated.
You ideally do not want to be making a decision on whether to update a status page or not during the first few minutes of an incident, bean counters inevitably tend to get involved to delay/not declare downtime if there is a manual process.
It is more likely the threshold is kept a bit higher than couple of minutes to reducing false positives rates, not because of manual updates.
Nah, _most_ status pages are hand updated to avoid false positives, and to avoid alerting customers when they otherwise would not have noticed. Very, very few organizations go out of their way to _tell_ customers they failed to meet their SLA proactively. GitHub's SLA remedy clause even stipulates that the customer is responsible for tracking availability, which GitHub will then work to confirm.
give the poor github ops folks a second to get things moving.