@udon I think it depends on how the CSS is linked to.
I tested it with my site and the Babylon Bee.
In the case of my site, it uses the CSS stored on Hozon Site (https://hozon.site/archive/1662531434/ryocafe.site/static/style.css), so CSS does get stored to the server.
However, in the case of Babylon Bee it still uses CSS hosted on Babylon Bee (for example: https://hozon.site/archive/1661640394/babylonbee.com/news/fbi-instructs-facebook-to-censor-posts-about-the-fbi-instructing-facebook-to-censor-posts-about-hunters-laptop.html).

Looking at the soyce code, the Bee is using full URLs for ASSets, while mine uses relative links, which I suspect to be the reason why.
So in theory if full paths get replaced by relative links during the archiving process, this would fix the issue.