Add match-start readiness barrier (Loading phase)

Gate the Lobby-to-world transition on a new MatchSubPhase.Loading before
Hide: movement stays frozen and the Hide countdown does not start until
every connected client has spawned all match avatars and applied their
paintings.

- MatchManager: Loading phase; matchLoadTimeout tunable; Match_BeginLoad
  broadcasts the respawned avatar NetworkObjectIds (+ generation tag),
  Match_Ready collects per-client ACKs (host self-checks locally); barrier
  coroutine in RunMatchPhases before Hide; disconnect/teardown cleanup.
- GameModeManager: freeze local player (movement/paint/tab) during Loading,
  restored via ActiveMode.Enter() on transition to Hide (no camera jump).
- NetworkPlayerSetup: treat Loading like Hide in ComputeVisible so a
  fast-loading client cannot reveal a hider early.
- MatchHud: "Loading" phase label.

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

Assets/Scripts/GameMode/GameModeManager.cs

@@ -61,6 +61,7 @@ public class GameModeManager : MonoBehaviour
     private int _activeIndex = -1;
     private bool _paused;
     private int _resumeIndex = -1;
+    private bool _loadFrozen; // true while the pre-match Loading barrier is holding the local player still
 
     /// <summary>The currently active mode (null before startup).</summary>
     public GameMode ActiveMode =>
@@ -322,6 +323,23 @@ public class GameModeManager : MonoBehaviour
         // switch key and Tick so Tab can't bootstrap a mode and no camera rig is driven until a bind.
         if (_activeIndex < 0) return;
 
+        // Pre-match loading barrier: hold the local player frozen (no movement, painting or mode switching)
+        // until every client has finished loading and the Hide phase begins. Re-asserted each frame so nothing
+        // sneaks input in; on release the active mode is re-entered to restore its intended control state
+        // without a camera jump (exactly like SetPaused's resume - the mode was never Exited).
+        if (MovementGated())
+        {
+            if (player) player.ControlEnabled = false;
+            if (painter) painter.PaintingEnabled = false;
+            _loadFrozen = true;
+            return;
+        }
+        if (_loadFrozen)
+        {
+            _loadFrozen = false;
+            ActiveMode?.Enter();
+        }
+
         // Resolution (the reveal window) is watch-only: force out of Paint and keep the switch key from
         // re-entering. No restore needed - the end-of-match respawn rebuilds the cycle at index 0.
         bool suppressPaint = PaintSuppressed();
@@ -355,6 +373,15 @@ public class GameModeManager : MonoBehaviour
                match.LocalSubPhase == MatchManager.MatchSubPhase.Resolution;
     }
 
+    /// <summary>True while the local match is in its pre-Hide LOADING barrier, during which the local player is
+    /// frozen (no movement, painting or mode switching) until every client has finished loading.</summary>
+    private bool MovementGated()
+    {
+        var match = MatchManager.Instance;
+        return match && match.MatchActive &&
+               match.LocalSubPhase == MatchManager.MatchSubPhase.Loading;
+    }
+
     /// <summary>First non-Paint mode index at or after <paramref name="start"/> (wrapping once through the
     /// cycle); -1 if the set has no non-paint mode (a degenerate paint-only configuration).</summary>
     private int FirstNonPaintFrom(int start)