PushAsync(TurnEnd|TurnEndFinal) fires FrameEmitted three times:
OpponentTurnStart + OpponentTurnEnd + OpponentJudge. Behaviour-identical
to the v1.2 case arm in BattleSession.ComputeResponses; just repackaged
as a participant. Other URIs are swallowed. Used by Phase 1 to preserve
v1.2 behaviour under the new abstraction; replaces the case-arm logic
in BattleSession in Task 7.
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