Valve does record your steamid go on Steam Privacy Policy Agreement it says it here.
Valve’s products, services and sites may employ cookies and other technologies such as web beacons and pixel tags. Cookies are bits of electronic information that can be transferred to a user's hard drive to customize a person's use of a product or online site, keep records of a user's access to an online site or product, or store information needed by the user on a regular basis. Use of cookies is typically associated with websites. For example, when you sign in to Steam, Valve stores your user id and a combination of your IP address and time of login as a cookie on your hard drive. This cookie allows you to move from page to page without having to sign in again on each page. Similarly, if you enter information during your session, such as age verification data, this will be stored as a cookie and you will not have to re-enter such information during that session. We may also use third party web site analytic tools that employ cookies to collect certain non-personally identifiable information concerning use of our websites, such as referring web site addresses, page views and browser types.