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

scripts/sync-branch.js

@@ -0,0 +1,22 @@
+const fs = require('fs');
+const { execSync } = require('child_process');
+
+let branch = 'test-gay';
+try {
+  branch = execSync('git rev-parse --abbrev-ref HEAD', { encoding: 'utf8' }).trim();
+} catch (_) {
+  try {
+    const head = fs.readFileSync('.git/HEAD', 'utf8');
+    const m = head.match(/ref:\s*refs\/heads\/([^\r\n]+)/);
+    if (m && m[1]) branch = m[1].trim();
+  } catch (__) {}
+}
+
+const versionData = {
+  branch,
+  version: '1.0.0',
+  updatedAt: new Date().toISOString()
+};
+
+fs.writeFileSync('version.json', JSON.stringify(versionData, null, 2) + '\n');
+console.log(`[sync-branch] Updated version.json with branch: ${branch}`);