Windows desktop app abruptly quits on closing last tab with Ctrl+W; align behavior with macOS via System Tray

Summary

On Windows (installed via .exe), pressing Ctrl+W when no editor tabs or terminals are open (or closing the last remaining tab) abruptly terminates the entire desktop application process without any confirmation or warning.

Motivation & Context

• Discrepancy with macOS: On macOS, closing windows via Cmd+W leaves the application active in the Dock / Tray, which allows reopening or restoring the application without terminating the background process.
• Accidental Closure: In Windows editor workflows, users frequently hit Ctrl+W to close tabs in succession. When the last tab closes, Ctrl+W directly kills the entire app and drops running background processes.
• Dedicated Exit Mechanism: T3 Code already provides a deliberate double Ctrl+Q gesture to exit the application cleanly.

Proposed Solution

1. Introduce native System Tray support on Windows with a context menu (Open / Quit) and click/double-click activation.
2. Update DesktopLifecycle to keep the background process alive on Windows upon window-all-closed, mirroring the macOS experience.

I have prepared a 2-part stacked PR to address this cleanly.

Start by reading DesktopLifecycle, especially the handling of window-all-closed, and compare the current Windows behavior with the stated macOS behavior. Review the existing two-part stacked PR if available. Done means closing the last tab or window on Windows keeps the process alive, provides a System Tray Open/Quit menu with activation, and preserves deliberate quitting through Ctrl+Q.