Add system tray / minimize-to-tray support for Claude Desktop (Windows)

Feature request

Right now Claude Desktop on Windows has no system tray icon. Every time it launches (auto-start or manual), it opens as a regular window — there's no way to keep it running in the background with just a tray icon, the way most Electron apps on Windows do (Discord, Slack, etc.).

Use case

I want Claude to start automatically with Windows but stay minimized to the tray instead of popping up a window on every boot. Currently the only options are "open as a window" or "don't auto-start at all."

Suggested behavior

• A tray icon that keeps the app running when the window is closed/minimized
• A setting to control whether closing the window quits the app or minimizes to tray
• Ideally, launch-at-login should default to starting minimized to tray

Windows build, app is distributed via Microsoft Store (MSIX).