Parent

Part of #1402. Depends on Phase 5.

Goal

Add a minimal app::adapters::tray::TrayAdapter under src-tauri/src/app/adapters/tray.rs that gives users a way back to the window once Phase 5 stops auto-quitting on close. No live metric rendering — that lands in #1401.

Workspace Context

This phase is entirely App-side: the tray adapter lives under src-tauri/src/app/adapters/ and is allowed to use tauri::*. It calls into the core crate for the Quit action introduced in Phase 5.

Scope

• Tray icon registered on app startup.
• Tray menu with Open (restore main window) and Quit (calls the Quit action from Phase 5, which ultimately drives core::monitoring::MonitoringState to Stopped).
• Left click on the tray icon also restores the window.
• All three platforms (Windows / macOS / Linux). On Linux, document any AppIndicator caveats discovered during implementation.

Out of Scope

• Live metric values in the tray (feat: live hardware metrics in system tray / menu bar (Stats-like widget) #1401).
• Pause / Resume monitoring entry — owned by feat: add background monitoring mode with system tray support #1275.
• Custom icons or theming.

Definition of Done

• Closing the main window leaves a tray icon visible.
• Clicking Open restores the window with state intact (size, position, current view).
• Quit exits the app cleanly through the lifecycle path from Phase 5.
• Graceful fallback when the user's environment does not support a tray (e.g. some Linux desktops): the app still quits cleanly via Quit from another path.

Notes

Once this lands, #1275 (background mode UX) and #1401 (live tray widget) can both proceed in parallel.