fix: steer-delivery starvation — continuation coalescing (claimSteers)

The bug (seen live): a teacher that ends every turn with a new pending quiz
keeps the wake pipeline's idle gates permanently closed — the steer sits in
'delivering result' forever while the learner answers check after check.

- claimSteers (server/jobs.ts): the chat-handler claims every queued,
  undelivered steer the instant a client turn wins the turn registry, and
  appends it after the learner's answer — conversion-safe, the answered
  quiz carries its output. Every answer flushes pending steers immediately.
- The pump keeps its post-idle duplicate-guard (re-check steerDelivered
  before firing), so a claim racing the pump converges to exactly one
  delivery either way.
- The stale-job sweep now skips chats with a turn in flight (a healthy but
  slow wake no longer gets falsely re-queued as 'recovering').
- Out-of-lane surgical touch (flagged for master review): the 3-line
  handleChatRequest seam (claim after beginTurn, persist+stream 'outgoing').
- Verified live end-to-end on the stuck session: answering the pending quiz
  fired the steer + wake turn within a second; job flipped done/delivered.

src/server/chat-handler.ts

@@ -3,7 +3,7 @@ import { createTeacherAgent, type TeacherAgent } from "../agent/teacher-agent.ts
 import { createJobRunner } from "../agent/subagents/runner.ts";
 import { createExtractionPipeline } from "../agent/subagents/extraction.ts";
 import { createTeacherTools } from "../agent/tools.ts";
-import { deliverJobResult, setJobRespawn, setTurnRunner } from "./jobs.ts";
+import { claimSteers, deliverJobResult, setJobRespawn, setTurnRunner } from "./jobs.ts";
 import { stores } from "./stores.ts";
 import { beginTurn, endTurn } from "./turn-liveness.ts";
 import { buildTeacherContext, persistTurn, triggerExtraction } from "./turn-service.ts";
@@ -71,6 +71,16 @@ export async function handleChatRequest(req: Request, agent?: TeacherAgent): Pro
 		return Response.json({ error: "A turn is already running for this session" }, { status: 409 });
 	}
 
+	// CONTINUATION COALESCING (async protocol §4, the delivery-starvation fix):
+	// steers finished while a quiz chain held the wake gates ride THIS turn —
+	// appended after the learner's answer (conversion-safe: the answer carries
+	// its output). Claiming happens after beginTurn, so this turn owns the
+	// registry and the write-ahead persist below makes the claim durable.
+	const steers = claimSteers(chatId);
+	const outgoing = (
+		steers.length > 0 ? [...(body.messages as UIMessage[]), ...steers] : body.messages
+	) as UIMessage[];
+
 	// Write-ahead persistence: the request body IS the client's canonical
 	// state, so it goes on disk BEFORE the stream starts. The learner's answer
 	// is durable the instant the request arrives — any remount, second tab, or
@@ -78,7 +88,7 @@ export async function handleChatRequest(req: Request, agent?: TeacherAgent): Pro
 	// returns mid-turn reads turnInFlight from the registry and re-attaches by
 	// polling instead of resurrecting the stale transcript.)
 	try {
-		stores.chatStore.saveMessages(chatId, body.messages as UIMessage[]);
+		stores.chatStore.saveMessages(chatId, outgoing);
 	} catch (err) {
 		console.error(`[chat ${chatId}] write-ahead persist failed:`, err);
 	}
@@ -97,7 +107,7 @@ export async function handleChatRequest(req: Request, agent?: TeacherAgent): Pro
 				}),
 				buildTeacherContext(stores.graphStore, chatId),
 			),
-		uiMessages: body.messages as UIMessage[],
+		uiMessages: outgoing,
 		// Tool-call validation failures are messages OUR schemas authored (the
 		// quiz authoring contract, unknown tools) — safe and useful in the
 		// transcript: they are exactly what the teacher saw and retried on. The