Add comprehensive backend test suite and helper access

GameList.Tests/AuthTests.cs

@@ -1,5 +1,4 @@
 using System.Net;
-using System.Net;
 using System.Net.Http.Json;
 using System.Text.Json;
 using GameList.Tests.Support;
@@ -47,4 +46,29 @@ public class AuthTests
 
         Assert.Equal(HttpStatusCode.Unauthorized, login.StatusCode);
     }
+
+    [Fact]
+    public async Task Register_validates_required_fields()
+    {
+        using var factory = new TestWebApplicationFactory();
+        var client = factory.CreateClientWithCookies();
+
+        var missing = await client.PostAsJsonAsync("/api/auth/register", new { Username = "", Password = "", DisplayName = "" });
+        Assert.Equal(HttpStatusCode.BadRequest, missing.StatusCode);
+
+        var badKey = await client.PostAsJsonAsync("/api/auth/register", new { Username = "u", Password = "p", DisplayName = "d", AdminKey = "wrong" });
+        Assert.Equal(HttpStatusCode.BadRequest, badKey.StatusCode);
+    }
+
+    [Fact]
+    public async Task Logout_clears_cookie()
+    {
+        using var factory = new TestWebApplicationFactory();
+        var client = factory.CreateClientWithCookies();
+        await client.RegisterAsync("logoutme");
+
+        var resp = await client.PostAsync("/api/auth/logout", null);
+        resp.EnsureSuccessStatusCode();
+        Assert.True(resp.Headers.TryGetValues("Set-Cookie", out var cookies) && cookies.Any(c => c.Contains("player")));
+    }
 }