Give each school its own people seed so composition no longer follows create order.

Co-authored-by: Cursor <cursoragent@cursor.com>

tests/HSchool.AppHost.Tests/SchoolApiTests.cs

@@ -371,9 +371,13 @@ public class SchoolApiTests(AppHostFixture fixture)
         return state;
     }
 
-    internal static async Task<SchoolResponse> CreateAsync(HttpClient client, string name, DateTime startDate)
+    internal static async Task<SchoolResponse> CreateAsync(
+        HttpClient client,
+        string name,
+        DateTime startDate,
+        int? seed = null)
     {
-        using var response = await PostAsync(client, name, startDate);
+        using var response = await PostAsync(client, name, startDate, seed);
         response.EnsureSuccessStatusCode();
 
         var created = await response.Content.ReadFromJsonAsync<SchoolResponse>(TestContext.Current.CancellationToken);
@@ -406,10 +410,14 @@ public class SchoolApiTests(AppHostFixture fixture)
         links = new[] { new { a = "yard", b = "office" } },
     };
 
-    private static Task<HttpResponseMessage> PostAsync(HttpClient client, string name, DateTime startDate) =>
+    private static Task<HttpResponseMessage> PostAsync(
+        HttpClient client,
+        string name,
+        DateTime startDate,
+        int? seed = null) =>
         client.PostAsJsonAsync(
             "/api/schools",
-            new { name, startDate },
+            seed is null ? (object)new { name, startDate } : new { name, startDate, seed },
             TestContext.Current.CancellationToken);
 
     private static async Task<string?> ProblemCodeAsync(HttpResponseMessage response)
@@ -418,7 +426,7 @@ public class SchoolApiTests(AppHostFixture fixture)
         return problem?.Code;
     }
 
-    internal sealed record SchoolResponse(int Id, string Name, DateTime GameTime, bool Running, byte SpeedIndex);
+    internal sealed record SchoolResponse(int Id, string Name, DateTime GameTime, bool Running, byte SpeedIndex, int Seed);
 
     internal sealed record SchoolsResponse(
         int MaxSchools,