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/components/recipe/cooking-assistant-panel.tsx

@@ -8,12 +8,15 @@ import { Sheet, SheetContent, SheetHeader, SheetTitle } from "@/components/ui/sh
 import { MessageCircle, Send, Bot, User } from "lucide-react";
 import ReactMarkdown from "react-markdown";
 import { cn } from "@/lib/utils";
+import { ChatHistorySearch } from "./chat-history-search";
 
 type Message = {
   role: "user" | "assistant";
   content: string;
 };
 
+type HistoryEntry = { role: "user" | "assistant"; content: string };
+
 export function CookingAssistantPanel() {
   const t = useTranslations("cookingChat");
   const [open, setOpen] = useState(false);
@@ -21,6 +24,18 @@ export function CookingAssistantPanel() {
   const [input, setInput] = useState("");
   const [loading, setLoading] = useState(false);
   const bottomRef = useRef<HTMLDivElement>(null);
+  const historyLoadedRef = useRef(false);
+
+  useEffect(() => {
+    if (!open || historyLoadedRef.current) return;
+    historyLoadedRef.current = true;
+    fetch("/api/v1/ai/chat-history?scope=general&limit=50")
+      .then((res) => (res.ok ? res.json() : null))
+      .then((json: { data?: HistoryEntry[] } | null) => {
+        if (json?.data?.length) setMessages(json.data.map((m) => ({ role: m.role, content: m.content })));
+      })
+      .catch(() => {});
+  }, [open]);
 
   useEffect(() => {
     if (open && bottomRef.current) {
@@ -83,10 +98,13 @@ export function CookingAssistantPanel() {
       <Sheet open={open} onOpenChange={setOpen}>
         <SheetContent side="right" className="w-full sm:w-[420px] flex flex-col p-0">
           <SheetHeader className="px-4 py-3 pr-10 border-b shrink-0">
-            <SheetTitle className="text-base flex items-center gap-2">
-              <Bot className="h-4 w-4 text-primary" />
-              {t("title")}
-            </SheetTitle>
+            <div className="flex items-center justify-between gap-2">
+              <SheetTitle className="text-base flex items-center gap-2">
+                <Bot className="h-4 w-4 text-primary" />
+                {t("title")}
+              </SheetTitle>
+              <ChatHistorySearch />
+            </div>
             <p className="text-xs text-muted-foreground text-left">{t("subtitle")}</p>
           </SheetHeader>