fix: dedupe same-id continuation copies in persistTurn (coalescing follow-up)

With a steer coalesced into a quiz-answer continuation, the steer sits AFTER
the assistant message being continued, so the SDK's onFinish list carries
the input copy AND the extended response copy as two entries with the SAME
id — persistTurn saved both, the jobs poller's syncFromServer imported the
dup, and React keyed a single message twice (the user's live test hit it).

withMessageIds now dedupes by id keeping the LAST occurrence — the SDK's
final merge state (a superset of the earlier copy) — which also yields the
right semantic shape: [user, steer, assistant(extended)].

Out-of-lane surgical touch (flagged for master review): turn-service.ts.

Squashed the live session's already-corrupted record by hand (same dedupe).

src/server/turn-service.ts

@@ -55,9 +55,23 @@ export function buildTeacherContext(graphStore: GraphStore, chatId: string): str
  * NEVER touched (the client's next POST still carries them verbatim).
  */
 export function withMessageIds(messages: UIMessage[]): UIMessage[] {
-	return messages.map((m) =>
+	const filled = messages.map((m) =>
 		m.id ? m : { ...m, id: `msg_${Date.now().toString(36)}_${crypto.randomUUID().slice(0, 8)}` },
 	);
+	// Same id twice = the SDK's continuation merge couldn't happen in place
+	// (continuation coalescing appends a user-role steer AFTER the assistant
+	// message being continued, so onFinish carries the input copy AND the
+	// extended response copy under one id). Keep the LAST occurrence — it is
+	// the SDK's final merge state (a superset of the earlier copy).
+	const seen = new Set<string>();
+	const deduped: UIMessage[] = [];
+	for (let i = filled.length - 1; i >= 0; i--) {
+		const m = filled[i]!;
+		if (seen.has(m.id)) continue;
+		seen.add(m.id);
+		deduped.unshift(m);
+	}
+	return deduped;
 }
 
 export function persistTurn(chatStore: ChatStore, chatId: string, messages: UIMessage[], isAborted: boolean): void {