As long as the admin password is kept the same, a running browser tab will keep its login credentials - no matter if - the system is rebooted - the system is shutdown and restarted - the system is installed onto another disk - even an old version is re-installed Any of these events should render the credentials "invalid", requiring a new login authentication.
This web user interface is using HTTP Basic authentication. The password will be transmitted to the web server with every request. If you re-install your system and you use the same password, then requests will continue to work. This is not a bug. It is designed like this.