Show sign-in window on first launch when user is not authenticated

**Summary**

When Coder Desktop is launched for the first time (or when the user is not signed in), the app should show the sign-in window instead of silently minimizing to the system tray. Currently, new users see no visible UI after launching the app, which makes it appear broken.

**Problem**

After a fresh install, launching Coder Desktop produces no visible window or taskbar entry. The app goes straight to the system tray as a background process. For a new user who has never used the app before:

1. There is no indication the app launched successfully
2. The user must discover the system tray icon (which Windows often hides behind the ^ overflow arrow)
3. The user must click the tray icon to find the sign-in prompt
4. The app cannot be used at all without signing in, so the silent tray behavior adds unnecessary friction

This leads users to believe the application failed to start — especially since Task Manager shows minimal CPU/memory activity, reinforcing the impression that nothing is happening.

**Proposed Behavior**

• First launch / not signed in: Show the sign-in window automatically. This gives the user a clear next step and confirms the app is running.
• Already authenticated: Continue the current behavior of going silently to the system tray.

Other system tray applications (such as Tailscale, 1Password) all show an onboarding or sign-in window on first launch before settling into tray-only mode.

issue にはファイル、テスト、エントリポイントが記載されていません。まず、Windows アプリの起動パスと認証状態の確認方法を追跡してください。未認証状態での初回起動時にサインインウィンドウが目に見える形で開き、認証済みの起動時にはそのままシステムトレイに進めば完了です。

索引モデルが issue の本文から書いたものです。