No, it can do more than that. For example it can tell the site whether the user is using a browser that is based on Chromium, which they can then use to deny you access if you don't. Since Manifest V3 has killed adblockers in Chromium-based browsers, this will mean if you need access to a site that does this, you will need to use a Chromium-based browser and see ads.
Looking at the proposal, it will also tell them which OS you use, making it even worse.