fix(mypage): wire mypage_id/select_type/mypage_id_list as strings

Prod capture (traffic_prod_misc_clicking.ndjson) shows all three
MyPageBgSetting fields arrive as decimal strings, not ints.  Update the
DTO from int/int/List<int> to string/string/List<string> with "0"/empty
defaults, and add a literal wire-shape round-trip test pinning the
exact JSON against the capture.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

SVSim.UnitTests/Wire/UserMyPageWireShape.cs

@@ -0,0 +1,40 @@
+using System.Text.Json;
+using SVSim.EmulatedEntrypoint.Models.Dtos;
+
+namespace SVSim.UnitTests.Wire;
+
+public class UserMyPageWireShape
+{
+    [Test]
+    public void MyPageBgSetting_serialization_emits_strings_matching_prod_capture()
+    {
+        var setting = new MyPageBgSetting
+        {
+            MyPageId = "1213410310",
+            SelectType = "1",
+            MyPageIdList = new List<string>
+            {
+                "1211410310", "1212410310", "1213410310", "1214410310",
+                "1215410310", "1216410310", "1217410310", "1218410310",
+            },
+        };
+
+        var options = new JsonSerializerOptions
+        {
+            PropertyNamingPolicy = JsonNamingPolicy.SnakeCaseLower,
+            DefaultIgnoreCondition = System.Text.Json.Serialization.JsonIgnoreCondition.WhenWritingNull,
+        };
+        var json = JsonSerializer.Serialize(setting, options);
+
+        // Prod capture line 12 / line 56 of traffic_prod_misc_clicking.ndjson, user_mypage_info.user_mypage_setting:
+        var expected =
+            "{\"mypage_id\":\"1213410310\"," +
+            "\"select_type\":\"1\"," +
+            "\"mypage_id_list\":[" +
+            "\"1211410310\",\"1212410310\",\"1213410310\",\"1214410310\"," +
+            "\"1215410310\",\"1216410310\",\"1217410310\",\"1218410310\"" +
+            "]}";
+
+        Assert.That(json, Is.EqualTo(expected));
+    }
+}