feat(auth): improve API key authentication flow (#11760)

Co-authored-by: gemini-code-assist[bot] <176961590+gemini-code-assist[bot]@users.noreply.github.com>

packages/cli/src/ui/auth/AuthDialog.test.tsx

@@ -191,7 +191,7 @@ describe('AuthDialog', () => {
         AuthType.USE_GEMINI,
       );
       expect(props.setAuthState).toHaveBeenCalledWith(
-        AuthState.Unauthenticated,
+        AuthState.AwaitingApiKeyInput,
       );
     });