Implement dead man's switch-style external health checks/monitoring to ping us in case of site going down, etc.

[Ambient-Impact]

While App Platform supports log forwarding, they're limited to three providers at the time of writing and those are primarily for internal logs; healthchecks.io is a fairly simple and straightforward dead man's switch-style service and has many integrations, including Discord and generic webhooks (e.g. for sending to our Discourse).