[Puzzles][Input] Update input handling to not mistakingly miss frames. Add debug frame input debugging.

Assets/Scripts/PuzzleManager.cs

@@ -3,7 +3,25 @@ using System.Collections.Generic;
 
 public class PuzzleManager : MonoBehaviour
 {
-    public static PuzzleManager Instance { get; private set; }
+    private static PuzzleManager _instance;
+    public static PuzzleManager Instance
+    {
+        get
+        {
+            if (_instance == null)
+            {
+                _instance = FindAnyObjectByType<PuzzleManager>();
+                if (_instance == null)
+                {
+                    var go = new GameObject("PuzzleManager");
+                    _instance = go.AddComponent<PuzzleManager>();
+                    DontDestroyOnLoad(go);
+                }
+            }
+            return _instance;
+        }
+    }
+
     private HashSet<PuzzleStepSO> completedSteps = new HashSet<PuzzleStepSO>();
     private HashSet<PuzzleStepSO> unlockedSteps = new HashSet<PuzzleStepSO>();
 
@@ -15,12 +33,12 @@ public class PuzzleManager : MonoBehaviour
 
     void Awake()
     {
-        if (Instance != null && Instance != this)
+        if (_instance != null && _instance != this)
         {
             Destroy(gameObject);
             return;
         }
-        Instance = this;
+        _instance = this;
         DontDestroyOnLoad(gameObject);
     }