If I build a service that needs a cookie to persist in the event of a user purging their cookies I don't think Google would accept that and just not delete it. The same is true for Google. If a user purges their cookies there shouldn't be any set afterwards.

However... what's probably happening here is that the cookie is being deleted but then created again immediately afterwards because something in the user's browser is connected to a Google server and that makes a new cookie if it detects the old one has gone away. The message in the tweet is informing the user that will happen. Arguably that's a reasonably useful notification - it stops the user mistakenly believing purging their cookies will log them out.

EDIT: Or, more likely, Google are actually storing the user's logged in state in localstorage or something, so clearing cookies won't log you out because there isn't a cookie.

I really hope not, no way Google can just change the nature of cookies in their browser to suit one of their services, it's just too much.