I can’t think of a way to do this with Github Pages alone.

I am in no way affiliated, but use Netlify to do exactly this (Bonus, it’s free).

Either using Snippet Injection (https://www.netlify.com/docs/inject-analytics-snippets/) if it is pure html/css/js.

Or using Environment Variables that get included in the build process for static site generation (https://www.netlify.com/docs/build-settings/).