feat(playwright): enable Playwright in production builds with custom browser path

Move Playwright from dev to production dependencies and implement robust browser
management for company deployment environment:

- Move playwright and playwright-core to dependencies
- Set PLAYWRIGHT_BROWSERS_PATH to user data directory before imports
- Add startup validation for Chromium browser with friendly error dialog
- Update build scripts to skip browser download during build process
- Configure electron-builder to unpack Playwright for native module access
- Add deployment documentation for browser setup in restricted environments

This allows manual browser installation in company environments where direct
downloads are blocked during build.

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

electron.vite.config.ts

@@ -4,13 +4,7 @@ import react from '@vitejs/plugin-react'
 import tailwindcss from '@tailwindcss/vite'
 
 export default defineConfig({
-  main: {
-    build: {
-      rollupOptions: {
-        external: ['playwright', 'playwright-core']
-      }
-    }
-  },
+  main: {},
   preload: {},
   renderer: {
     resolve: {