Fix G key (playBestSolution never awaited async bestSolution), add menu exit

- playBestSolution() called bestSolution() (now async, hits the server)
  without await/async — got a Promise object back, .moves was undefined,
  autoPlayStep() bailed on its first tick. G silently did nothing.
- No way back to the menu from gameplay — add 🏠 HUD button + M key,
  cancels any in-flight search/autoplay before switching screens.
- settings-save button now shows "Сохраняю…" and disables itself during
  the request — previously gave no feedback while the fetch was in
  flight, looked like a dead button even though it worked (confirmed via
  server logs/DB — the save itself was never broken).

php/index.php

@@ -13,6 +13,8 @@
   canvas { border: 3px solid #e94560; border-radius: 12px; box-shadow: 0 0 20px rgba(233,69,96,0.4); }
   #hud { display: flex; gap: 20px; color: #e94560; font-size: 16px; font-weight: bold; }
   #hud span { background: rgba(233,69,96,0.1); padding: 8px 16px; border-radius: 20px; border: 1px solid rgba(233,69,96,0.3); }
+  #menu-btn { cursor: pointer; }
+  #menu-btn:hover { background: rgba(233,69,96,0.25) !important; }
   #controls { color: #aaa; font-size: 13px; }
   kbd { background: #1a1a2e; border: 1px solid #e94560; border-radius: 4px; padding: 2px 6px; color: #e94560; }
   #solve-overlay { position: fixed; inset: 0; background: rgba(10,10,21,0.75); display: flex; justify-content: center; align-items: center; z-index: 10; }
@@ -124,6 +126,7 @@
     <span id="level-name">Уровень 1</span>
     <span id="box-count">📦 0/0</span>
     <span id="moves-count">👣 0</span>
+    <span id="menu-btn" title="В меню">🏠</span>
   </div>
   <div id="controls">
     <kbd>← → ↑ ↓</kbd> или <kbd>WASD</kbd> — движение &nbsp;
@@ -131,7 +134,8 @@
     <kbd>P</kbd> — пред. &nbsp;
     <kbd>R</kbd> — рестарт &nbsp;
     <kbd>F</kbd> — автопоиск (<kbd>Esc</kbd> — отмена) &nbsp;
-    <kbd>G</kbd> — лучшее сохранённое решение
+    <kbd>G</kbd> — лучшее сохранённое решение &nbsp;
+    <kbd>M</kbd> — в меню
   </div>
 </div>
 
@@ -1722,9 +1726,9 @@ function autoPlayStep() {
   tryMove(dx, dy);
 }
 
-function playBestSolution() {
+async function playBestSolution() {
   if (autoSolveActive || levelComplete || solveState || playerMoving || boxes.some(b => b.moving)) return;
-  const best = bestSolution(LEVELS[currentLevel].name);
+  const best = await bestSolution(LEVELS[currentLevel].name);
   if (!best) { alert('Нет сохранённых решений для этого уровня — сначала пройди его (F или руками)'); return; }
   startFlatPlayback(best.moves);
 }
@@ -2080,6 +2084,7 @@ window.addEventListener('keydown', e => {
   if (key === 'p') { currentLevel=(currentLevel-1+LEVELS.length)%LEVELS.length; loadLevel(currentLevel); e.preventDefault(); return; }
   if (key === 'f') { startAutoSolve(); e.preventDefault(); return; }
   if (key === 'g') { playBestSolution(); e.preventDefault(); return; }
+  if (key === 'm') { backToMenu(); e.preventDefault(); return; }
 
   // Стрелки и WASD
   if (['arrowup','arrowdown','arrowleft','arrowright','w','a','s','d'].includes(key)) {
@@ -2149,14 +2154,31 @@ document.getElementById('start-begin').addEventListener('click', () => {
 });
 document.getElementById('end-menu').addEventListener('click', () => showScreen('screen-menu'));
 
+// Выход в меню из игры — гасим поиск/автопроигрывание, если шли, иначе
+// они продолжат тикать в фоне за скрытым экраном.
+function backToMenu() {
+  if (solveState) cancelAutoSolve();
+  autoSolveActive = false;
+  autoPlayMoves = null;
+  showScreen('screen-menu');
+}
+document.getElementById('menu-btn').addEventListener('click', backToMenu);
+
 document.getElementById('settings-save').addEventListener('click', async () => {
   const name = document.getElementById('settings-name-input').value.trim();
   if (!name) return;
+  const btn = document.getElementById('settings-save');
+  btn.disabled = true;
+  const originalText = btn.textContent;
+  btn.textContent = 'Сохраняю…';
   try {
     await apiPost('set_name', { name });
     showScreen(settingsReturnTo === null ? 'screen-menu' : settingsReturnTo);
   } catch {
     alert('Не удалось сохранить имя — сервер недоступен');
+  } finally {
+    btn.disabled = false;
+    btn.textContent = originalText;
   }
 });
 document.getElementById('settings-name-input').addEventListener('keydown', e => {