GitHub pages and relative paths

You’ll need to use Jekyll.

Copying verbatim from the relevant documentation:

Sometimes it’s nice to preview your Jekyll site before you push your
gh-pages branch to GitHub. However, the subdirectory-like URL
structure GitHub uses for Project Pages complicates the proper
resolution of URLs. Here is an approach to utilizing the GitHub
Project Page URL structure (username.github.io/project-name/) whilst
maintaining the ability to preview your Jekyll site locally.

1. In _config.yml, set the baseurl option to /project-name – note the leading slash and the absence of a trailing slash.

2. When referencing JS or CSS files, do it like this: {{ site.baseurl}}/path/to/css.css – note the slash immediately following
   the variable (just before “path”).

3. When doing permalinks or internal links, do it like this: {{ site.baseurl }}{{ post.url }} – note that there is no slash between
   the two variables.

4. Finally, if you’d like to preview your site before committing/deploying using jekyll serve, be sure to pass an empty
   string to the --baseurl option, so that you can view everything at
   localhost:4000 normally (without /project-name at the beginning):
   jekyll serve --baseurl ''

This way you can preview your site locally from the site root on
localhost, but when GitHub generates your pages from the gh-pages
branch all the URLs will start with /project-name and resolve
properly.

(Apparently someone figured this out only a few months ago.)