First, I don't think you're being realistic about how tracking works nowadays. Google will will link your new "anonymous" account to your established tracking profile as soon as you access it from a device or geographical location associated with your existing account. This is true even if you never visit any Google owned domain, through the magic of shared tracking IDs.

Second, your position rests on the assumption that this hypothetical federal ID will be mandatory. How will it be "required"? By whom? If the government makes a federal oauth, and it works well, sure, some webapps might require it, but they can also just require your identity today. I think you haven't wrapped your mind around the idea that any big tech company that doesn't already have your identity doesn't want it. Google doesn't care about your SSN, they care about your browsing and shopping history, but the day they decide they want it, they'll demand it, and you'll comply or go without Google services (and they'll probably get it from data sharing partner anyway). None of that would change due to what I'm proposing.