Internal setter; defaults to AwaitingInitNetwork. PvP needs A and B to
progress through the handshake states independently, which the
session-level BattleSession.Phase can't model. Session migration to read
realFrom.Phase is the next task.
Lifts the WS read loop, SIO encode/decode, per-WS OutboundSequencer +
InboundTracker, and SIO ack out of BattleSession into a participant.
PushAsync(noStock=false) assigns playSeq via the sequencer; noStock=true
bypasses it. FrameEmitted fires on each deduplicated inbound envelope.
The existing BattleSession keeps its own copy of the WS code for now;
Task 9 cuts the handler over to use BattleSessionV2 + RealParticipant
and Task 10 deletes the old BattleSession + duplicate code.
