feat(battle-node): RealParticipant session-finished signal + Pvp cascade

RealParticipant gains _sessionFinished TCS + MarkSessionFinished /
AwaitSessionFinishedAsync. PvP first-arriver's handler awaits the
signal instead of calling self.RunAsync (which the session does
internally on the same instance — double-call would race the WS read).

BattleSession.RunAsync branches on Type: Pvp uses WhenAny + synthesize
BattleFinish(Win) to survivor + WhenAll(drain); Scripted/Bot keep
Phase 1's WhenAll-everything semantics. Disconnect cascade now drives
end-of-battle when a WS drops without a graceful Retire.

SVSim.BattleNode/Sessions/Participants/RealParticipant.cs

@@ -57,6 +57,33 @@ public sealed class RealParticipant : IBattleParticipant, IHasHandshakePhase
 
     public event Func<MsgEnvelope, CancellationToken, Task>? FrameEmitted;
 
+    private readonly TaskCompletionSource<bool> _sessionFinished
+        = new(TaskCreationOptions.RunContinuationsAsynchronously);
+
+    /// <summary>Called by the second arriver's handler (in a finally block) after
+    /// session.RunAsync completes. Signals the first arriver's handler that it can
+    /// return and let the HTTP request complete (which closes the WS).</summary>
+    internal void MarkSessionFinished() => _sessionFinished.TrySetResult(true);
+
+    /// <summary>Awaited by the first arriver's handler instead of calling RunAsync
+    /// (the session already calls RunAsync on this instance from the second arriver's
+    /// handler context — calling it twice would race the WS read loop). Returns when
+    /// either MarkSessionFinished fires or the passed CT cancels.</summary>
+    internal Task AwaitSessionFinishedAsync(CancellationToken ct)
+    {
+        if (_sessionFinished.Task.IsCompleted) return _sessionFinished.Task;
+        var tcs = new TaskCompletionSource<bool>(TaskCreationOptions.RunContinuationsAsynchronously);
+        var reg = ct.Register(() => tcs.TrySetCanceled(ct));
+        _sessionFinished.Task.ContinueWith(t =>
+        {
+            reg.Dispose();
+            if (t.IsCompletedSuccessfully) tcs.TrySetResult(true);
+            else if (t.IsFaulted) tcs.TrySetException(t.Exception!.InnerExceptions);
+            else tcs.TrySetCanceled();
+        }, TaskContinuationOptions.ExecuteSynchronously);
+        return tcs.Task;
+    }
+
     public RealParticipant(WebSocket ws, long viewerId, MatchContext context,
         ILogger<RealParticipant> log)
     {