With not really knowing all the details, I’m inclined to say no, your hardware processors do not make any difference here. It should not show up to the browser. Here is a comparison site (https://privacytests.org/) that lists quite a lot of things that websites try to do to get info and here is another (https://coveryourtracks.eff.org/) that should show what kind of fingerprint you leave. Problem being that there can be tactics that aren’t listed in those, of course. Also note that not all browsers are equal in covering user privacy.
On the other hand, one reason that I can think of why this could be done by the website, is to stave off AI crawlers (see: Testing anubis to prevent LLM bots from taking down source.puri.sm)