#101112 made round members take their turns concurrently. That changed what
a group chat IS: later speakers in a round no longer saw earlier speakers'
replies, so bots answered the user independently instead of building on
each other. Group rooms are serial round-robin by design — this restores the
pre-#101112 round engine (group-rounds.ts, group-chat.ts, group-chat-view.tsx,
their tests, and the docs) byte-for-byte.
What stays from #101112: the per-turn poll wakes on the member session's
terminal frame (message.complete / error via host.onEvent) instead of
sleeping a fixed 2s between session.resume reads; 5s timer kept as backstop.
That is a pure latency fix with no change to room semantics.
Live A/B (real tui_gateway over WS, 4 members, one serial round):
2s poll 32.5s -> push-woken 22.5s. The remaining time is model latency.
Refs #92760
Teknium
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