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/SmartCollectionControllerTests.cs

@@ -54,7 +54,7 @@ public class SmartCollectionControllerTests
         var created = result.ShouldBeOfType<CreatedResult>();
         created.StatusCode.ShouldBe(201);
         created.Location.ShouldBe("/api/smart-collections/7");
-        created.Value.ShouldBe(vm);
+        created.Value.ShouldBe(new SmartCollectionResponseModel(7, "Kids", "tag:family"));
     }
 
     [Test]
@@ -98,7 +98,8 @@ public class SmartCollectionControllerTests
             new UpdateSmartCollectionRequest("Updated", "tag:updated"),
             CancellationToken.None);
 
-        result.ShouldBeOfType<OkObjectResult>().Value.ShouldBe(vm);
+        result.ShouldBeOfType<OkObjectResult>().Value
+            .ShouldBe(new SmartCollectionResponseModel(8, "Updated", "tag:updated"));
         await _mediator.Received(1).Send(
             Arg.Is<UpdateSmartCollection>(c =>
                 c.Id == 8 && c.Name == "Updated" && c.Query == "tag:updated"),
@@ -166,7 +167,8 @@ public class SmartCollectionControllerTests
 
         IActionResult result = await _controller.GetById(4, CancellationToken.None);
 
-        result.ShouldBeOfType<OkObjectResult>().Value.ShouldBe(vm);
+        result.ShouldBeOfType<OkObjectResult>().Value
+            .ShouldBe(new SmartCollectionResponseModel(4, "Kids", "tag:kids"));
     }
 
     [Test]