fix: cooking chatbot button too high; chatbots leaked underlying model name

Moved the homepage cooking-assistant button from bottom-24 to bottom-16 —
still clears the recipe list's floating bulk-action bar, just not as far.

Both chat system prompts (cooking-chat and the per-recipe chat) now
explicitly identify as "Epicure" and are told never to name the underlying
model/provider if asked — previously they'd just answer honestly with
whatever the model calls itself.

Verified locally: screenshotted the new button position, and asked "what
model or AI are you" through the real UI — response identified as Epicure
with no model name.

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

@@ -40,7 +40,7 @@ export async function POST(req: NextRequest) {
   const result = await withAiQuota(session!.user.id, session!.user.tier as "free" | "pro", () =>
     generateText({
       model,
-      system: `You are a helpful culinary assistant answering general cooking questions — not tied to any specific recipe (techniques, substitutions, timing, equipment, food safety, etc). If a question has nothing to do with cooking or food, politely redirect. Keep answers under 200 words. Respond in ${lang}.${bioContext}`,
+      system: `You are Epicure, a helpful culinary assistant answering general cooking questions — not tied to any specific recipe (techniques, substitutions, timing, equipment, food safety, etc). If asked who you are or what model/AI you're built on, say you're Epicure — never name the underlying model or provider. If a question has nothing to do with cooking or food, politely redirect. Keep answers under 200 words. Respond in ${lang}.${bioContext}`,
       prompt: parsed.data.question,
     })
   );

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

@@ -76,7 +76,7 @@ ${stepList || "None listed"}
   const result = await withAiQuota(session!.user.id, session!.user.tier as "free" | "pro", () =>
     generateText({
       model,
-      system: `You are a helpful culinary assistant. Answer questions about the following recipe concisely and accurately. If a question is not related to the recipe or cooking, politely redirect. Keep answers under 200 words. Respond in ${lang}.
+      system: `You are Epicure, a helpful culinary assistant. Answer questions about the following recipe concisely and accurately. If asked who you are or what model/AI you're built on, say you're Epicure — never name the underlying model or provider. If a question is not related to the recipe or cooking, politely redirect. Keep answers under 200 words. Respond in ${lang}.
 
 ${recipeContext}${bioContext}`,
       prompt: parsed.data.question,

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

@@ -70,10 +70,10 @@ export function CookingAssistantPanel() {
       <Button
         variant="default"
         size="icon"
-        // bottom-24 (not bottom-6, like the per-recipe chat button) clears the
+        // bottom-16 (not bottom-6, like the per-recipe chat button) clears the
         // recipe list's floating bulk-action bar, which occupies the bottom-4
         // to bottom-8 band while select mode is active.
-        className="fixed bottom-24 right-6 h-12 w-12 rounded-full shadow-lg z-40"
+        className="fixed bottom-16 right-6 h-12 w-12 rounded-full shadow-lg z-40"
         onClick={() => setOpen(true)}
         aria-label={t("ariaLabel")}
       >