CSS file hosting for a website is usually simple: put the stylesheet in the ZIP and reference it from HTML with a relative path. A typical archive contains index.html and css/site.css, with <link rel="stylesheet" href="css/site.css"> in the page.
Why styles disappear after upload
The common causes are a stylesheet outside the ZIP, an incorrect path, or a filename case mismatch. CSS/site.css is not the same path as css/site.css on a Linux server.
Open the browser network panel after publishing. The missing stylesheet URL tells you exactly what the page requested. Match that URL to the archive, fix the HTML or filename, and publish a new ZIP.