Yes, all these forms should handle existing names...

but the author's own website doesn't (url: xn--stpie-k0a81a.com, bottom of the page: "© 2024 ę ń. All rights reserved.")

I think the bottom of the page is you missing the joke. It's showing only the name letters that get rejected everywhere else. Similarly for the URL, the URL renders his name correctly when you browse to it in a modern browser. What you've copied is the canonical fallback for unicode.