Wire the 409 merge-retry transport into the chat (the one-line seam)

chat.tsx now uses createChatTransport(chatId): a send racing the wake
pipeline waits for the in-flight turn, merges onto the fresh server
record, and re-POSTs instead of surfacing the 409 banner. Also fixes the
transport's import to the core barrel (shell import law).

The optional "server-ahead heal" line in the jobs poller was considered
and skipped: the racing turn IS the wake turn, whose completion flips the
job to done within a poll tick or two — the existing settle-triggered
syncFromServer already heals the post-merge gap within ~1-2s. The extra
record fetch on every poll tick would double poll traffic for a path the
settle sync already covers.

components/chat-transport.ts

@@ -21,7 +21,7 @@
  * a future "server-ahead" heal in the poller). Rare path; self-heals.
  */
 import { DefaultChatTransport } from "ai";
-import type { TeacherUIMessage } from "@/src/core/ui-message";
+import type { TeacherUIMessage } from "@/src/core";
 
 /** How often to poll turnInFlight while the racing turn runs. */
 const TURN_POLL_MS = 500;

components/chat.tsx

@@ -2,7 +2,8 @@
 
 import { createContext, Fragment, useCallback, useEffect, useLayoutEffect, useMemo, useRef, useState } from "react";
 import { useChat } from "@ai-sdk/react";
-import { DefaultChatTransport, isToolUIPart, lastAssistantMessageIsCompleteWithToolCalls } from "ai";
+import { isToolUIPart, lastAssistantMessageIsCompleteWithToolCalls } from "ai";
+import { createChatTransport } from "@/components/chat-transport";
 import { useStickToBottomContext } from "use-stick-to-bottom";
 import {
 	Conversation,
@@ -81,7 +82,7 @@ export function Chat({
 		useChat<TeacherUIMessage>({
 			id: chatId,
 			messages: initialMessages,
-			transport: new DefaultChatTransport({ api: "/api/chat", body: { chatId } }),
+			transport: createChatTransport(chatId),
 			// After the learner answers (addToolOutput), automatically send the
 			// continuation request so the teacher reacts to the answer.
 			sendAutomaticallyWhen: lastAssistantMessageIsCompleteWithToolCalls,