feat(viewer): add MyPageBgSelectType + MyPageBgId scalars + MyPageBgRotation owned collection

Adds BGType persistence (0=Deck/1=CustomBG/2=RandomBG) to Viewer via two scalar
columns and an owned collection keyed (ViewerId, Slot). Two persistence tests
confirm round-trip and zero-defaults on fresh viewers.

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

SVSim.UnitTests/Persistence/MyPageBgPersistenceTests.cs

@@ -0,0 +1,61 @@
+using Microsoft.EntityFrameworkCore;
+using Microsoft.Extensions.DependencyInjection;
+using SVSim.Database;
+using SVSim.Database.Models;
+using SVSim.UnitTests.Infrastructure;
+
+namespace SVSim.UnitTests.Persistence;
+
+public class MyPageBgPersistenceTests
+{
+    [Test]
+    public async Task Viewer_round_trips_mypage_bg_scalars_and_rotation_pool()
+    {
+        using var factory = new SVSimTestFactory();
+        long viewerId = await factory.SeedViewerAsync();
+
+        using (var seedScope = factory.Services.CreateScope())
+        {
+            var ctx = seedScope.ServiceProvider.GetRequiredService<SVSimDbContext>();
+            var viewer = await ctx.Viewers
+                .Include(v => v.MyPageBgRotation)
+                .FirstAsync(v => v.Id == viewerId);
+            viewer.MyPageBgSelectType = 2;
+            viewer.MyPageBgId = 1213410310;
+            viewer.MyPageBgRotation.Add(new MyPageBgRotationEntry { Slot = 0, BgId = 1211410310 });
+            viewer.MyPageBgRotation.Add(new MyPageBgRotationEntry { Slot = 1, BgId = 1212410310 });
+            viewer.MyPageBgRotation.Add(new MyPageBgRotationEntry { Slot = 2, BgId = 1213410310 });
+            await ctx.SaveChangesAsync();
+        }
+
+        using var verifyScope = factory.Services.CreateScope();
+        var ctx2 = verifyScope.ServiceProvider.GetRequiredService<SVSimDbContext>();
+        var roundtrip = await ctx2.Viewers
+            .Include(v => v.MyPageBgRotation)
+            .AsNoTracking()
+            .FirstAsync(v => v.Id == viewerId);
+
+        Assert.That(roundtrip.MyPageBgSelectType, Is.EqualTo(2));
+        Assert.That(roundtrip.MyPageBgId, Is.EqualTo(1213410310));
+        Assert.That(roundtrip.MyPageBgRotation.OrderBy(r => r.Slot).Select(r => r.BgId),
+            Is.EqualTo(new[] { 1211410310, 1212410310, 1213410310 }));
+    }
+
+    [Test]
+    public async Task Viewer_fresh_viewer_has_zero_defaults_and_empty_rotation()
+    {
+        using var factory = new SVSimTestFactory();
+        long viewerId = await factory.SeedViewerAsync();
+
+        using var scope = factory.Services.CreateScope();
+        var ctx = scope.ServiceProvider.GetRequiredService<SVSimDbContext>();
+        var viewer = await ctx.Viewers
+            .Include(v => v.MyPageBgRotation)
+            .AsNoTracking()
+            .FirstAsync(v => v.Id == viewerId);
+
+        Assert.That(viewer.MyPageBgSelectType, Is.EqualTo(0));
+        Assert.That(viewer.MyPageBgId, Is.EqualTo(0));
+        Assert.That(viewer.MyPageBgRotation, Is.Empty);
+    }
+}