feat: multiple named conversations for the cooking assistant

The general assistant had exactly one conversation per user forever
(recipeId null on chat_messages) — no way to start fresh or organize
by topic. Adds an ai_conversations table (title, timestamps) and a
nullable conversationId FK on chat_messages; the assistant panel gets
a conversations menu to create/switch/rename/delete, auto-titling a
new conversation from its first question.

Per-recipe chat is untouched — each recipe already has one natural
thread, so multi-conversation support only applies to the homepage
assistant. Pre-existing general messages (no conversationId) aren't
migrated into the new model and won't appear in the conversation list.

Requires migration 0042 to run against a live DB — not applied in
this sandbox (no Docker here); run `pnpm db:migrate`.

v0.43.0

apps/web/app/api/v1/ai/conversations/[id]/route.ts

@@ -0,0 +1,45 @@
+import { NextRequest, NextResponse } from "next/server";
+import { z } from "zod";
+import { db, aiConversations, eq, and } from "@epicure/db";
+import { requireSessionOrApiKey } from "@/lib/api-auth";
+
+type Params = { params: Promise<{ id: string }> };
+
+const RenameSchema = z.object({ title: z.string().max(100).nullable() });
+
+export async function PATCH(req: NextRequest, { params }: Params) {
+  const { session, response } = await requireSessionOrApiKey(req);
+  if (response) return response;
+  const { id } = await params;
+
+  const body = await req.json() as unknown;
+  const parsed = RenameSchema.safeParse(body);
+  if (!parsed.success) {
+    return NextResponse.json({ error: "Validation error" }, { status: 400 });
+  }
+
+  const [updated] = await db
+    .update(aiConversations)
+    .set({ title: parsed.data.title?.trim() || null, updatedAt: new Date() })
+    .where(and(eq(aiConversations.id, id), eq(aiConversations.userId, session!.user.id)))
+    .returning();
+
+  if (!updated) return NextResponse.json({ error: "Not found" }, { status: 404 });
+
+  return NextResponse.json({ id: updated.id, title: updated.title });
+}
+
+export async function DELETE(req: NextRequest, { params }: Params) {
+  const { session, response } = await requireSessionOrApiKey(req);
+  if (response) return response;
+  const { id } = await params;
+
+  const [deleted] = await db
+    .delete(aiConversations)
+    .where(and(eq(aiConversations.id, id), eq(aiConversations.userId, session!.user.id)))
+    .returning({ id: aiConversations.id });
+
+  if (!deleted) return NextResponse.json({ error: "Not found" }, { status: 404 });
+
+  return NextResponse.json({ ok: true });
+}