refactor(auth): extract AuthPasswordForm and AuthCodeForm to features

- Create auth-password feature with login/register form
- Create auth-code feature with email+code verification form
- Extract getApiErrorMessage to shared lib
- Simplify AuthPage to pure UI composer with tabs
- Update tests for new component structure
- All 40 tests passing

client/src/shared/lib/get-api-error-message.ts

@@ -0,0 +1,8 @@
+export function getApiErrorMessage(err: unknown): string | null {
+  if (!err || typeof err !== 'object') return null
+  const anyErr = err as Record<string, unknown>
+  const response = anyErr.response as Record<string, unknown> | undefined
+  const data = response?.data as Record<string, unknown> | undefined
+  const msg = data?.error
+  return typeof msg === 'string' ? msg : null
+}