feat: PlayMode 切换 + bind/unbind/setPlayMode 携带北京时间

主要改动（与 iOS SDK 1:1 对齐）：
- 新增 BeijingTimeProvider：苏宁公开 API → header Date → 本地+8h 三级 fallback；
  5 秒缓存 + Mutex 单飞复用
- 新增 PlayMode enum (SINGLE=0, LOOP=1)
- DeviceInfo 增加可选 loop 字段（旧固件无此字段时为 null）
- DeviceInfoService.bind/unbind/setPlayMode 共用 payload，带 time 字段；
  loop == null 时严格省略 key（与 expo zod.optional 对齐）
- DuooomiBleSDK.setPlayMode(mode, userId)：复用 BIND_DEVICE 命令通道，
  isActivated 守卫；成功后自动刷新 deviceInfo
- Demo 增加 Single / Loop 按钮（gated by isActivated）

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

sdk/src/main/kotlin/com/duooomi/ble/DuooomiBleSDK.kt

@@ -5,6 +5,7 @@ import com.duooomi.ble.core.*
 import com.duooomi.ble.models.*
 import com.duooomi.ble.protocol.CommandType
 import com.duooomi.ble.services.*
+import com.duooomi.ble.utils.BeijingTimeProvider
 import com.duooomi.ble.utils.BleLog
 import kotlinx.coroutines.*
 import kotlinx.coroutines.flow.*
@@ -45,7 +46,8 @@ class DuooomiBleSDK(context: Context, val config: DuooomiBleConfig) {
 
     private val bleClient = BleClient(context)
     private val protocolService = BleProtocolService(bleClient)
-    private val deviceInfoService = DeviceInfoService(protocolService)
+    private val timeProvider = BeijingTimeProvider()
+    private val deviceInfoService = DeviceInfoService(protocolService, timeProvider)
     private val fileTransferService = FileTransferService(protocolService)
     private val aniConverter = AniConverter(config)
     private val firmwareService = FirmwareService(config)
@@ -229,6 +231,36 @@ class DuooomiBleSDK(context: Context, val config: DuooomiBleConfig) {
         return resp
     }
 
+    /**
+     * 切换播放模式（0=单播 / 1=循环播放）。
+     *
+     * 复用 [CommandType.BIND_DEVICE] (0x0F) 命令通道；响应类型为 [BindingResponse]。
+     * 成功后自动刷新一次 `deviceInfo`（含最新 `loop` 字段），与 expo 端行为对齐。
+     *
+     * 前置：必须已 [bind] 完成（`isActivated == true`）。
+     * `bind` / `unbind` / `setPlayMode` 共享 0x0F / 0x12 opId 通道，**不能并发**。
+     */
+    suspend fun setPlayMode(mode: com.duooomi.ble.models.PlayMode, userId: String): BindingResponse {
+        ensureConnected()
+        if (!_isActivated.value) {
+            BleLog.w("setPlayMode called before bind (isActivated=false)", "Command")
+            throw DuooomiBleError.BindingFailed("Device not bound; call bind(userId) first")
+        }
+        BleLog.d("Sending setPlayMode (mode=$mode, userId=$userId)", "Command")
+        val data = sendAndWait(CommandType.BIND_DEVICE) {
+            deviceInfoService.setPlayMode(userId, mode)
+        }
+        val resp = BindingResponse.fromJson(parseJsonResponse(data))
+        if (resp.success != 1) {
+            BleLog.w("setPlayMode failed: device rejected", "Command")
+            throw DuooomiBleError.BindingFailed("Set play mode failed")
+        }
+        BleLog.i("setPlayMode success: mode=$mode", "Command")
+        // 自动刷新 deviceInfo（含最新 loop 字段）
+        runCatching { getDeviceInfo() }
+        return resp
+    }
+
     suspend fun unbind(userId: String): UnbindResponse {
         ensureConnected()
         BleLog.d("Sending unbind (userId=$userId)", "Command")