feat: Implement PWA install prompt with platform-specific handling and dismissal persistence.

docs/development/devlog/2025-12-18-004600_pwa_install_prompt.md

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+# PWA Install Prompt Implementation Plan
+
+## Objective
+Implement a user interface that prompts the user to install the application as a PWA on supported devices (primarily Android/Chrome).
+
+## Tasks
+1. Create `src/client/src/components/PWAInstallPrompt.tsx` that:
+   - Listens for `beforeinstallprompt` event.
+   - Displays a custom UI (toast/banner) when the event is captured.
+   - Calls `prompt()` on the event object when the user clicks "Install".
+   - Handles the user's choice.
+2. Integrate `PWAInstallPrompt` into `App.tsx`.
+3. Verify `vite.config.ts` PWA settings (already done, looks good).
+
+## Implementation Details
+- The component will use a fixed position styling (bottom right/center) to be noticeable but not blocking.
+- It will use existing design system (Tailwind).
+
+## Status
+- [x] Create Component
+- [x] Integrate into App
+- [x] Update Config
+- **Completed**: 2025-12-18