Refactor GameRepository and GameManager architecture, introduce Player model, and update dependency registration in Program.cs.

API/Models/Game/Game.cs

@@ -13,7 +13,7 @@ public class Game(Coordinates gFs, SixDigitInt gameCode)
 {
     public string Id { get; init; } = Guid.NewGuid().ToString();
     public SixDigitInt GameCode { get; } = gameCode;
-    public string?[] PlayerConnectionIds { get; set; } = new string?[2];
+    public Player?[] PlayerConnectionIds { get; set; } = new Player?[2];
     public GameState State { get; private set; } = GameState.Lobby;
     public GameField Field { get; } = new(gFs);
 }

API/Models/Game/GameField.cs

@@ -1,9 +1,9 @@
 namespace API.Models.Game;
 
-public class Coordinates
+public readonly struct Coordinates(int x, int y)
 {
-    public int X;
-    public int Y;
+    public readonly int X = x;
+    public readonly int Y = y;
 }
 
 public enum PlaceResult

API/Models/Game/Player.cs

@@ -0,0 +1,7 @@
+namespace API.Models.Game;
+
+public class Player
+{
+    public string Name { get; set; }
+    public string ConnectionId { get; set; }
+}