Google Login form clears LocalStorage values

Question

I am working with Login with Google, I observed that Google Login form clears a LocalStorage, SessionStorage and session values. Is there any way I can keep this values? or any other ways to keep some values to use after login. I tried for Stackoverflow site too, gave me same result. I set some values and tried to get. I got the values

But when I clicked on Login with Google and tried, I get nothing. On Login with google form of same site