feat: Wave C - pi-native steer/follow-up delivery

Delivery now rides pi's OWN follow-up queue when a run is live, and a
carry-everything idle wake otherwise. One registry, two vehicles;
claimSteers and continuation coalescing are deleted (owner rulings,
2026-09-26: follow-ups only; one queue; the wake is the only appender).

THE LIVE RUN (vehicle 1): the chat-handler registers the streaming
turn's agent (registerLiveAgent, next to registerTurn); the pump hands
every eligible queued marker to agent.followUp() - pi polls that queue
when the run would otherwise stop, injects the markers
(message_start/message_end on the live wire), and CONTINUES the same
run. followUpMode "all" joins every handed marker in one continuation
turn. The question stopper runs before the follow-up poll, so an open
quiz is never overridden - a handed marker strands at settlement and
waits (today's pacing). probe-handoffs never take this path (the
handoff must START the teacher's run - a record-level branch).

SETTLEMENT RECONCILIATION: settleSteers(chatId, persisted) at onFinish
(after unregisterLiveAgent) resolves+flips entries the run delivered
and returns stranded ones to pending - the registry stays the truth;
the dead agent's queued copy is abandoned. This is what makes the
handoff safe: pi owns no retry for a stranded follow-up.

THE IDLE WAKE (vehicle 2): waitForIdle (unchanged gates) then ONE turn
carrying EVERY pending marker as its input appends - dequeue-at-fire
(the Wave B regression lesson: the wake run's own follow-up poll must
never see its own cargo; a 409 pushes the cargo back and retries).

CLIENT: applyWireEvent now upserts non-assistant messages by id, so
in-run injected markers render live instead of dropping until settle.

Tests: jobs 44/44 (live handoff, settlement stranding, handoff-waits,
one-wake-carries-all); chat-flow 23/23 (the double-append pin drives
the real pump through the new input); session-core 28/28 (custom-role
wire appends). Full suite 997/997, tsc/lint/build green.

Live smoke (PORT=3004): research job delivered mid-probe - parked
behind the dangling questions exactly per semantics, landed once on
the open gates, teacher folded the brief in and re-dispatched; the
second (good) result rendered the full 10-source brief card and the
lesson continued from it. No duplicate ids anywhere in the record.

Known gap flagged to owner (NOT from this change): the server accepts
malformed answer events via raw API (answers without the answers[]
shape) and AnsweredCard then crashes the page render - surfaced by the
smoke's scripted answers, repaired by hand in the scratch record.

src/core/input-events.ts

@@ -42,8 +42,12 @@ export type ChatInput =
 	| { type: "verdict"; accepted: boolean; note?: string }
 	| { type: "continue" };
 
-/** A wake-pipeline steer delivery — same turn composition, server-origin. */
-export type SteerInput = { type: "steer"; steer: LhMessage };
+/** A wake-pipeline steer delivery — same turn composition, server-origin.
+ *  Wave C (2026-09-26): the idle wake carries EVERY queued marker as its
+ *  input appends — with claimSteers deleted, the pump's wake is the only
+ *  steer appender left (the in-run path hands markers to pi's own
+ *  follow-up queue instead, so it never builds an input event). */
+export type SteerInput = { type: "steers"; steers: LhMessage[] };
 
 /** Every input the turn composition accepts. */
 export type TurnInput = ChatInput | SteerInput;