feat: persist AI chat history, add search across it

Both chat panels (per-recipe and the general cooking assistant) previously
kept messages in component state only — closing the sheet or reloading
the page lost everything. Both POST routes now persist question+answer
pairs to a new chat_messages table (recipeId null for the general
assistant), and both panels load their own history back on open.

New GET /api/v1/ai/chat-history (scoped by recipeId, or scope=general for
the homepage assistant, or neither to search across everything) backs a
new search control in both panels' header — debounced, shows matched
messages with date and (when searching across everything) which recipe
they belonged to.

Verified locally: asked a real question, closed and reopened the panel
and confirmed the conversation reloaded, then searched a keyword from
that conversation and confirmed both the question and answer surfaced
in the results dropdown.

apps/web/app/api/v1/ai/cooking-chat/route.ts

@@ -1,6 +1,7 @@
 import { NextRequest, NextResponse } from "next/server";
 import { z } from "zod";
 import { generateText } from "ai";
+import { db, chatMessages } from "@epicure/db";
 import { requireSession } from "@/lib/api-auth";
 import { applyRateLimit } from "@/lib/rate-limit";
 import { withAiQuota, resolveAiConfigOrError } from "@/lib/ai/ai-error";
@@ -46,5 +47,10 @@ export async function POST(req: NextRequest) {
   );
   if (!result.ok) return result.response;
 
+  void db.insert(chatMessages).values([
+    { id: crypto.randomUUID(), userId: session!.user.id, recipeId: null, role: "user", content: parsed.data.question },
+    { id: crypto.randomUUID(), userId: session!.user.id, recipeId: null, role: "assistant", content: result.data.text },
+  ]).catch((err) => console.error("[cooking-chat] failed to persist chat history", err));
+
   return NextResponse.json({ answer: result.data.text });
 }