After changing the password, the account does not automatically log out

After I change the password on my ChatGPT account, ChatGPT doesn’t automatically log out from the webpage. Instead, the entire page becomes unusable, with no clickable buttons.

I need to clear the browser cookies to be able to see the login button again.

This is a screenshot of the webpage after changing the chatGPT account password. I need to clear the browser cookies to make the login button reappear.