Our internal team members complain some times with "Hubspot is not working", so I would love to have a webhook/api to get the status of the hubspot API, so we can show a badge or something to our users and they understand inmediatly that the issue comes from Hubspot and not from our API.
Currently, this is not something that we support. The best way is probably to check in on the status page to keep updated.
On this note, I located a similar idea posted on our HubSpot idea page: HubSpot Community - Ability to subscribe to all status updates - HubSpot Community. If you haven't already, I'd recommend getting it an upvote so that it's visible to the HubSpot product team and other HubSpot customers and developers. Hopefully this will gather more interest.