Add conversion statues shown in resolution phase

In Conversion mode, capture a snapshot (pose index + paint) of each hider
at conversion time and materialize a frozen, painted statue at the found
spot for the resolution phase, independent of the now-hunter avatar.

- MatchStatue.cs (new): server-init pose/paint, network-driven pose then
  freeze, reveal-gate (hidden until paint applied), kills inherited sim.
- PlayerPaintSync: _isStatue (sibling auto-detect) suppresses the three
  auto-behaviours so MatchStatue drives the paint flow deterministically.
- MatchManager: statuePrefab; capture in ConvertToHunter; spawn on
  resolution enter; despawn + record clear on EndMatch/teardown/start.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

Assets/Scripts/Network/PlayerPaintSync.cs

@@ -138,7 +138,18 @@ public class PlayerPaintSync : NetworkBehaviour
     // spawn), applied in LateUpdate once this fresh painter is ready. Null = nothing to carry.
     private byte[] _pendingCarry;
 
-    private void Awake() => _painter = GetComponentInChildren<MeshPainter>(true);
+    // True when this receiver sits on a MatchStatue: a statue drives its painting explicitly (the server
+    // loads the captured snapshot then broadcasts it), so the owner-carry take, the client auto snapshot-
+    // request and the no-carry blank publish are all suppressed to keep them from racing that push.
+    private bool _isStatue;
+
+    private void Awake()
+    {
+        _painter = GetComponentInChildren<MeshPainter>(true);
+        // Detected from the sibling component so no inspector flag can be forgotten on the prefab.
+        var statue = GetComponentInChildren<MatchStatue>(true);
+        _isStatue = statue;
+    }
 
     public override void OnNetworkSpawn()
     {
@@ -151,7 +162,7 @@ public class PlayerPaintSync : NetworkBehaviour
             _painter.OnHistoryCheckpoint += OnLocalCheckpoint;
             _painter.OnHistoryRestore += OnLocalRestore;
 
-            if (MatchManager.Instance) _pendingCarry = MatchManager.Instance.TakeCarriedPaint();
+            if (MatchManager.Instance && !_isStatue) _pendingCarry = MatchManager.Instance.TakeCarriedPaint();
         }
         else
         {
@@ -178,8 +189,8 @@ public class PlayerPaintSync : NetworkBehaviour
             _heightApplyPending = true;
 
             // The host's replica already holds the full paint via the live stream; only a genuine
-            // late joiner needs the baseline pulled over.
-            if (!IsServer)
+            // late joiner needs the baseline pulled over. A statue never pulls - the server pushes it.
+            if (!IsServer && !_isStatue)
             {
                 _awaitingSnapshot = true;
                 if (logSync) LogSync("late joiner: requesting baseline snapshot");
@@ -293,7 +304,7 @@ public class PlayerPaintSync : NetworkBehaviour
         // avatar must still hand every peer an explicit (blank) snapshot, otherwise its body stays hidden
         // forever behind the receiver-side reveal gate. Carry/manual-load already publish (and set the
         // cutoff), so this only fires for the no-carry case.
-        if (_publishedCutoff.Value < 0 && _pendingCarry == null && _painter && _painter.IsPaintReady)
+        if (_publishedCutoff.Value < 0 && _pendingCarry == null && !_isStatue && _painter && _painter.IsPaintReady)
             BroadcastLoadedPaint();
 
         // Delta-only publish: the NetworkVariable dirties only on an actual change.