feat(flutter): send timezone on login + app-start + weekly

Flutter client posts FlutterTimezone.getLocalTimezone() to
PUT /api/me/timezone on every setSession (login / register success)
and on every AuthController.build (app cold-start with valid
session), when the locally-stored tz_last_sent_at is >7 days old.
Cadence tracked in flutter_secure_storage so it survives app
restarts.

Failures swallowed: the server's UTC default + last-known value
keep the scheduler functioning until the next attempt.

Completes the client side of #392 Half B (per-user timezone
scheduling).

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

flutter_client/lib/api/endpoints/me.dart

@@ -38,4 +38,12 @@ class MeApi {
     );
     return SystemPlaylistsStatus.fromJson(r.data ?? const {});
   }
+
+  /// PUT /api/me/timezone — submit the device's IANA timezone. The
+  /// scheduler uses this to fire the user's daily playlist build at
+  /// 03:00 in their local time. See AuthController._sendTimezoneIfStale
+  /// for the weekly cadence trigger.
+  Future<void> putTimezone(String timezone) async {
+    await _dio.put<void>('/api/me/timezone', data: {'timezone': timezone});
+  }
 }