It may be good to have the Log In button right below the password field - I kept wanting to click the Log Out button after typing my password since it was the next field there ... feels a bit awkward to have to go back to the top and click there to log in
also - it would be awesome if you could use a ternary and display the Log Out button only if the user is logged in and vice versa - the Log In button only if the user is not logged in
looks fine! 👍
Just a couple of suggestions to consider: