How do I change a user after login (e.g. su root)?

You cannot. SFTP protocol does not allow this. With SCP you can potentially execute su root from the console dialog. But most of the servers (maybe all) require TTY terminal to execute su command. It makes them sure that a human is sitting by the client. Unfortunatelly WinSCP cannot use TTY terminal, because it is not compatible both with SFTP and SCP protocol.