Create a static status page on yourserver.com/status.html and write:
If you can't read this, it means the status of yourserver.com is: DOWN
However, status pages are first and foremost marketing tools, so I wouldn't expect anyone setting such mechanism up.
All the mainstream browsers have already said they won't ever implement it.
Do you know what is their rationale?
The slightly slower page loads is one extra round trip to the DNS server (that is supposed to be close to you). It can be solved at the DNS side, and last time I looked, about a decade ago, was indeed solved at the default configuration of most open-source servers. But the large providers don't use the default configuration of their servers.
https://twitter.com/StackStatus/status/1575844926884962305?s...
The old status page https://stackstatus.tumblr.com is up, but not updated.