Add Capacitor Android packaging (APK) for Cafe Bazaar / Myket

- Next static export (output: export) wrapped by Capacitor; appId
  com.bargevasat.app, appName «برگ وسط»
- android/ native project + @capacitor/app; hardware back handled by
  CapacitorBack (back a screen, exit at home)
- npm scripts (cap:sync, android:open, android:apk), ANDROID.md
- Gradle Maven-mirror init-script template (dl.google.com/Maven Central are
  blocked in Iran — same reason NuGet is mirrored)

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src/app/page.tsx

@@ -13,6 +13,7 @@ import { ShopScreen } from "@/components/screens/ShopScreen";
 import { ChatScreen } from "@/components/screens/ChatScreen";
 import { AuthScreen } from "@/components/screens/AuthScreen";
 import { DailyRewardModal } from "@/components/online/DailyRewardModal";
+import { CapacitorBack } from "@/components/CapacitorBack";
 import { useSessionStore } from "@/lib/session-store";
 import { useGameStore } from "@/lib/game-store";
 import { useOnlineStore } from "@/lib/online-store";
@@ -55,6 +56,7 @@ export default function Page() {
     <>
       {renderScreen(screen)}
       <DailyRewardModal />
+      <CapacitorBack />
       {loading && null}
     </>
   );

src/components/CapacitorBack.tsx

@@ -0,0 +1,29 @@
+"use client";
+
+import { useEffect } from "react";
+import { Capacitor } from "@capacitor/core";
+import { App } from "@capacitor/app";
+import { useUIStore } from "@/lib/ui-store";
+
+/**
+ * Maps the Android hardware back button to in-app navigation:
+ * go back a screen, or exit the app when already at home.
+ * No-op on web (Capacitor.isNativePlatform() is false).
+ */
+export function CapacitorBack() {
+  useEffect(() => {
+    if (!Capacitor.isNativePlatform()) return;
+    let remove: (() => void) | undefined;
+    App.addListener("backButton", () => {
+      if (useUIStore.getState().screen === "home") {
+        App.exitApp();
+      } else {
+        window.history.back();
+      }
+    }).then((h) => {
+      remove = () => h.remove();
+    });
+    return () => remove?.();
+  }, []);
+  return null;
+}