A lot of external status services just send a HTTP request to a certain url, if it succeeds then it's up, if it errors or times out then it's down. They also usually let you check if TCP ports do the usual handshake thing if you aren't using HTTP.

The response time can also be used to check if a site is running slower than usual too, and if you have a use for it you can usually specify the required response code for success.

Although I wouldn't be surprised if GitHub has some per-server analytics they can also use to estimate the load, but Instatus would work as described above.

Sometimes these sorts of things are referred to as health checks, if you're looking for search terms. For example Docker can be set up to poll a container's web server every few minutes, and mark it as unhealthy it if it stops replying using the HEALTHCHECK instruction in the Dockerfile.