The correct action is to disable the button while the request is in flight so it can't be clicked a second time. Otherwise you won't see "user already logged in", because the user won't be logged in until the previous request returns (a race condition).
If you have a race condition, "correct action" is to solve that, because you shouldn't be papering over server-side bugs with client-side Javascript (and yes, it's a bug, because I shouldn't see an error page if I press the back button after logging in (and trying to navigate to what I was doing before logging in) either, which I still see quite often)
For users with JS disabled, your solution seems good.