Codex [ T3 Code ] Add system tray icon with context menu and status indicator

[cerredz]

/claim #859

Summary

• Adds a desktop DesktopTray service wired into Electron startup with system tray creation, platform-specific click handling, Show/Hide, New Chat, Open Recent Project, and Quit actions.
• Adds a shared tray-state IPC contract plus preload bridge so the renderer publishes active project, recent projects, and connection status for tooltip/menu/icon updates.
• Routes tray menu actions through the existing desktop menu-action bridge and handles New Chat / recent project selection in AppSidebarLayout.
• Adds focused desktop tray unit coverage for state normalization, tooltip text, menu labels, and action dispatch strings.

Verification

• npx --yes bun run --filter @t3tools/desktop test -- src/window/DesktopTray.test.ts
• npx --yes bun run --filter @t3tools/desktop typecheck
• npx --yes bun run --filter @t3tools/web typecheck
• npx --yes bun run --filter @t3tools/contracts typecheck
• npx --yes bun run fmt:check -- apps/desktop/src/window/DesktopTray.ts apps/desktop/src/window/DesktopTray.test.ts apps/desktop/src/app/DesktopApp.ts apps/desktop/src/main.ts apps/desktop/src/ipc/channels.ts apps/desktop/src/ipc/DesktopIpcHandlers.ts apps/desktop/src/ipc/methods/window.ts apps/desktop/src/preload.ts apps/web/src/components/AppSidebarLayout.tsx packages/contracts/src/ipc.ts apps/web/src/components/settings/SettingsPanels.browser.tsx apps/web/src/localApi.test.ts
• git diff --check HEAD~1..HEAD

npx --yes bun run lint -- <touched files> is blocked by the repository's TypeScript oxlint plugin failing to load under the available Node runtime: ERR_UNKNOWN_FILE_EXTENSION for oxlint-plugin-t3code/index.ts.

I did not add _contributor.json because it asks for hidden runtime instructions rather than product code.