feat(ui): display current git branch in browser tab, header, and nav tabs

- Add branch indicator in browser tab title ([test-gay] GaC-Srtool...)
- Add dynamic tab switching updates preserving branch prefix in browser title
- Add branch badge in brand header and right-aligned branch pill in navigation tabs
- Add scripts/sync-branch.js and version.json for automated branch detection

package.json

@@ -4,8 +4,9 @@
   "description": "Companion Web Management Dashboard & FreeSR Tool for GaC-hkrpg-go",
   "main": "index.html",
   "scripts": {
-    "dev": "npx serve . -l 5173",
-    "start": "npx serve . -l 5173",
+    "sync-branch": "node scripts/sync-branch.js",
+    "dev": "node scripts/sync-branch.js && npx serve . -l 5173",
+    "start": "node scripts/sync-branch.js && npx serve . -l 5173",
     "serve": "npx serve . -l 5173"
   },
   "keywords": [