If that’s the explanation, the solution is to logout the browser when the user logs out of a google service. That would follow the users expectation (based on

If that’s the explanation, the solution is to logout the browser when the user logs out of a google service. That would follow the users expectation (based on their observation). Logging the user into the browser, on the other hand, is not directly related. And potentially unexpected for the user. They could have had one without the other.