feat(api): #288 wrap raw VMs, nullable-honest DTOs, search pageNum

24 #nullable enable flips across ErsatzTV.Core/Api; Collection/Schedule/
SmartCollection/Resolution VMs wrapped in ResponseModels (Version now
header-only, SPA-verified); pageNum threaded into GET /api/search.

Refs #288 #197

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

ErsatzTV.Tests/Controllers/ResolutionControllerTests.cs

@@ -47,6 +47,31 @@ public class ResolutionControllerTests
             ]);
     }
 
+    [Test]
+    public async Task GetResolutionByName_Should_Return_ResponseModel_Not_ViewModel()
+    {
+        _mediator.Send(Arg.Any<GetResolutionByName>(), Arg.Any<CancellationToken>())
+            .Returns(Option<ResolutionViewModel>.Some(new ResolutionViewModel(1, "1920x1080", 1920, 1080, false)));
+
+        ActionResult<ResolutionResponseModel> result =
+            await _controller.GetResolutionByName("1920x1080", CancellationToken.None);
+
+        var ok = result.Result.ShouldBeOfType<OkObjectResult>();
+        ok.Value.ShouldBe(new ResolutionResponseModel(1, "1920x1080", 1920, 1080, false));
+    }
+
+    [Test]
+    public async Task GetResolutionByName_Should_Return_404_For_None()
+    {
+        _mediator.Send(Arg.Any<GetResolutionByName>(), Arg.Any<CancellationToken>())
+            .Returns(Option<ResolutionViewModel>.None);
+
+        ActionResult<ResolutionResponseModel> result =
+            await _controller.GetResolutionByName("nope", CancellationToken.None);
+
+        result.Result.ShouldBeOfType<NotFoundResult>();
+    }
+
     [Test]
     public async Task Create_Should_Return_201_With_Location_And_Body()
     {