PROFILEPHOTO: profilePhotoUrl computed field on GerbilDto

GET /gerbils/{id}: loads first photo by sortOrder (2 queries, no N+1).
GET /gerbils list: batch-loads first photos for the page in one IN query.
profilePhotoUrl = /photos/files/{fileName} or null. No migration.
3 new tests: no-photo=null, sortOrder priority, list batch.

GerbilManager.Tests/GerbilProfilePhotoTests.cs

@@ -0,0 +1,83 @@
+using System.Net;
+using System.Net.Http.Json;
+using System.Text.Json;
+using System.Text.RegularExpressions;
+using GerbilManagerWebAPI.Models;
+using Microsoft.Extensions.DependencyInjection;
+
+namespace GerbilManager.Tests;
+
+/// <summary>profilePhotoUrl: computed field on GerbilDto — first photo by sortOrder, or null.</summary>
+public class GerbilProfilePhotoTests : IClassFixture<ApiFactory>
+{
+    private readonly HttpClient _client;
+    private readonly ApiFactory _factory;
+
+    public GerbilProfilePhotoTests(ApiFactory factory)
+    {
+        _factory = factory;
+        _client = factory.CreateClient();
+    }
+
+    private static Guid ExtractId(string json) =>
+        Guid.Parse(Regex.Match(json, "\"id\":\"([^\"]+)\"").Groups[1].Value);
+
+    private static string? GetStr(JsonElement el, string prop) =>
+        el.TryGetProperty(prop, out var v) && v.ValueKind == JsonValueKind.String
+            ? v.GetString() : null;
+
+    private async Task<Guid> CreateGerbil(string name)
+    {
+        var resp = await _client.PostAsync("/gerbils", JsonContent.Create(new { name, gender = "female" }));
+        Assert.Equal(HttpStatusCode.Created, resp.StatusCode);
+        return ExtractId(await resp.Content.ReadAsStringAsync());
+    }
+
+    private void InsertPhotos(Guid gerbilId, params (string fileName, int sortOrder)[] photos)
+    {
+        using var scope = _factory.Services.CreateScope();
+        var db = scope.ServiceProvider.GetRequiredService<ApplicationContext>();
+        foreach (var (fn, so) in photos)
+            db.GerbilPhotos.Add(new GerbilPhoto
+            {
+                Id = Guid.NewGuid(), GerbilId = gerbilId,
+                FileName = fn, SortOrder = so, CreatedAt = DateTimeOffset.UtcNow,
+            });
+        db.SaveChanges();
+    }
+
+    [Fact]
+    public async Task GetById_without_photos_returns_null_profilePhotoUrl()
+    {
+        var id = await CreateGerbil("NoPhoto");
+        var json = await _client.GetStringAsync($"/gerbils/{id}");
+        var el = JsonDocument.Parse(json).RootElement;
+        Assert.True(el.TryGetProperty("profilePhotoUrl", out var v));
+        Assert.Equal(JsonValueKind.Null, v.ValueKind);
+    }
+
+    [Fact]
+    public async Task GetById_with_photos_returns_lowest_sortOrder_url()
+    {
+        var id = await CreateGerbil("PhotoGerbil");
+        InsertPhotos(id, ("second.jpg", 1), ("first.jpg", 0));
+
+        var json = await _client.GetStringAsync($"/gerbils/{id}");
+        var el = JsonDocument.Parse(json).RootElement;
+        Assert.Equal("/photos/files/first.jpg", GetStr(el, "profilePhotoUrl"));
+    }
+
+    [Fact]
+    public async Task GetList_returns_profilePhotoUrl_without_n_plus_1()
+    {
+        var id = await CreateGerbil("ListPhoto");
+        InsertPhotos(id, ("list-photo.jpg", 0));
+
+        var json = await _client.GetStringAsync("/gerbils");
+        var root = JsonDocument.Parse(json).RootElement;
+        var items = root.GetProperty("items").EnumerateArray().ToList();
+        var gerbil = items.FirstOrDefault(x => GetStr(x, "id") == id.ToString());
+        Assert.NotEqual(default, gerbil);
+        Assert.Equal("/photos/files/list-photo.jpg", GetStr(gerbil, "profilePhotoUrl"));
+    }
+}