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.UnitTests/BattleNode/Sessions/Participants/RealParticipantTests.cs

@@ -127,6 +127,48 @@ public class RealParticipantTests
             "B's Phase must not change when A's Phase is set.");
     }
 
+    [Test]
+    public async Task AwaitSessionFinishedAsync_returns_when_MarkSessionFinished_fires()
+    {
+        var ws = new TestWebSocket();
+        var p = new RealParticipant(ws, viewerId: 1, FixtureCtx(),
+            NullLogger<RealParticipant>.Instance);
+
+        var awaiter = p.AwaitSessionFinishedAsync(CancellationToken.None);
+        p.MarkSessionFinished();
+
+        await awaiter; // should complete promptly
+        Assert.Pass();
+    }
+
+    [Test]
+    public void AwaitSessionFinishedAsync_cancels_on_token()
+    {
+        var ws = new TestWebSocket();
+        var p = new RealParticipant(ws, viewerId: 1, FixtureCtx(),
+            NullLogger<RealParticipant>.Instance);
+
+        using var cts = new CancellationTokenSource();
+        var awaiter = p.AwaitSessionFinishedAsync(cts.Token);
+        cts.Cancel();
+
+        Assert.That(async () => await awaiter, Throws.InstanceOf<OperationCanceledException>());
+    }
+
+    [Test]
+    public async Task MarkSessionFinished_is_idempotent()
+    {
+        var ws = new TestWebSocket();
+        var p = new RealParticipant(ws, viewerId: 1, FixtureCtx(),
+            NullLogger<RealParticipant>.Instance);
+
+        p.MarkSessionFinished();
+        p.MarkSessionFinished(); // should not throw
+
+        await p.AwaitSessionFinishedAsync(CancellationToken.None);
+        Assert.Pass();
+    }
+
     private static MatchContext FixtureCtx() => new(
         SelfDeckCardIds: Enumerable.Range(1, 30).Select(_ => 100_011_010L).ToList(),
         ClassId: "1", CharaId: "1", CardMasterName: "card_master_node_10015",