chore: move widget source into sidecar repo (widget-src/)

Widget builds from widget-src/ → public/widget.js
Vite outDir updated to ../public
.gitignore excludes node_modules

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

widget-src/package.json

@@ -0,0 +1,18 @@
+{
+  "name": "helix-engage-widget",
+  "version": "0.1.0",
+  "private": true,
+  "scripts": {
+    "dev": "vite",
+    "build": "vite build",
+    "preview": "vite preview"
+  },
+  "dependencies": {
+    "preact": "^10.25.0"
+  },
+  "devDependencies": {
+    "@preact/preset-vite": "^2.9.0",
+    "typescript": "^5.7.0",
+    "vite": "^6.0.0"
+  }
+}