Auto-closing feedback dialog after login – how to indicate this to the user?

My login dialog has four states:

  • 'Form' - for actually filling in the user details
  • Loading - waiting for the server response
  • Failed - feedback & a retry button to take you back to the 'form'
  • Success - feedback, and an okay button to close

It was correctly pointed out that the success dialog is more frustrating than useful. It's just an extra button to press. There's some good answers here.

I still want to show feedback of the success, beyond the minor changes to the UI (profile pic/user name/logout button in the bar in the top right).

The easiest thing is to simply remove the okay buttons, and close the login dialog after a small time. So, at the moment it looks like this in the success state:

enter image description here

And after a second it closes itself.

It works well, but I can't help but think it feels a bit strange. There's no indication to the user that this dialog is going to close in a second. How can I indicate that this is going to happen? A little countdown/progress bar animation?