As a simple example, the hit gives them your IP address. Often, this is all they need in order to identify you. (My IP address is technically dynamic, but remains fixed for weeks at a time. And... even if I use a different browser to sign into Facebook, they still have that IP address as well as the relevant timeframe for my possession of it.

I could spin up a VM and route the FB or non-FB traffic through a proxy, but I haven't reached that point, yet. (Probably, foolishly and to my detriment...)

P.S. In other words, state is already stored on their servers, not (or rather, in addition to) your browser.