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

js/app.js

@@ -841,6 +841,7 @@ function applyTranslations() {
     renderAvatarsGrid();
   }
   loadEquipment();
+  updateDocumentTitle();
 }
 
 // Setup Language Selector
@@ -6328,6 +6329,7 @@ function setupTabs() {
       if (targetContent) {
         targetContent.classList.add('active');
         state.activeTab = targetId;
+        updateDocumentTitle(targetId);
 
         // On-demand tab refresh
         if (targetId === 'tab-avatars') {
@@ -7278,6 +7280,85 @@ function setupEvents() {
   });
 }
 
+// ==========================================
+// Git Branch Detection & Browser Tab Title
+// ==========================================
+let currentGitBranch = 'test-gay';
+
+function updateDocumentTitle(tabId = state.activeTab || 'tab-dashboard') {
+  const branchPrefix = currentGitBranch ? `[${currentGitBranch}] ` : '';
+  const tabNames = {
+    'tab-dashboard': 'GaC-Srtool — Ultimate Star Rail Server & Build Manager',
+    'tab-avatars': `👥 ${t('tabAvatars') || 'ตัวละคร'} | GaC-Srtool`,
+    'tab-equipment': `🗡️ ${t('tabEquipment') || 'กรวยแสง & รีลิกส์'} | GaC-Srtool`,
+    'tab-persistent': `💾 ${t('tabPersistent') || 'จัดการเซฟ GaC'} | GaC-Srtool`,
+    'tab-exrank': `⚡ ${t('tabExrank') || 'สกิลพิเศษ Ex-Rank'} | GaC-Srtool`,
+    'tab-json': `📝 ${t('tabJson') || 'จัดการไฟล์ JSON'} | GaC-Srtool`,
+    'tab-settings': `⚙️ ${t('tabSettings') || 'ตั้งค่า'} | GaC-Srtool`
+  };
+  const titleBody = tabNames[tabId] || 'GaC-Srtool — Ultimate Star Rail Server & Build Manager';
+  document.title = `${branchPrefix}${titleBody}`;
+}
+
+function applyBranchToUI(branch) {
+  state.currentBranch = branch;
+  currentGitBranch = branch;
+
+  // 1. Browser Tab Title (<title> & document.title)
+  updateDocumentTitle();
+
+  // 2. Header Brand Badge
+  const headerBadge = document.getElementById('header-branch-badge');
+  if (headerBadge) {
+    headerBadge.textContent = branch;
+    headerBadge.style.display = 'inline-flex';
+  }
+
+  // 3. Nav Tabs Branch Indicator
+  const navBadge = document.getElementById('nav-branch-name');
+  if (navBadge) {
+    navBadge.textContent = branch;
+  }
+}
+
+async function initGitBranchDisplay() {
+  // 1. URL Query Param ?branch=...
+  const urlParams = new URLSearchParams(window.location.search);
+  const branchFromUrl = urlParams.get('branch');
+  if (branchFromUrl) {
+    applyBranchToUI(branchFromUrl.trim());
+    return;
+  }
+
+  // 2. version.json (Generated by sync-branch or git commit)
+  try {
+    const res = await fetch('version.json?t=' + Date.now());
+    if (res.ok) {
+      const data = await res.json();
+      if (data && data.branch) {
+        applyBranchToUI(data.branch.trim());
+        return;
+      }
+    }
+  } catch (_) {}
+
+  // 3. .git/HEAD (if served locally by dev server)
+  try {
+    const headRes = await fetch('.git/HEAD?t=' + Date.now());
+    if (headRes.ok) {
+      const headText = await headRes.text();
+      const match = headText.match(/ref:\s*refs\/heads\/([^\r\n]+)/);
+      if (match && match[1]) {
+        applyBranchToUI(match[1].trim());
+        return;
+      }
+    }
+  } catch (_) {}
+
+  // 4. Fallback
+  applyBranchToUI(currentGitBranch);
+}
+
 // Background Ping Loop
 function startPingLoop() {
   setInterval(() => {
@@ -7287,6 +7368,7 @@ function startPingLoop() {
 
 // Initialize Application
 async function init() {
+  await initGitBranchDisplay();
   await loadCachedGachabaseData({
     idbGet,
     idbSet,