Open the old website in Chrome or any modern browser. It doesn't matter if it's running on
localhost,
a staging server behind a VPN, or even just a saved
.html file on your desktop.
HTML to Figma doesn't need a public URL.
If the site no longer exists at all, you can work directly from the source files. Open the HTML in a browser via
File > Open
or a simple local server like python3 -m http.server.