refactor: extract system prompts and add extended prompt for Opus/Haiku 4.5 (#71)

- Extract system prompts to dedicated lib/system-prompts.ts module
- Add extended system prompt (~4000 tokens) for models with higher cache minimums (Opus 4.5, Haiku 4.5)
- Clean up debug logs while preserving informational and cache-related logs
- Improve code formatting and organization in chat route

components/chat-panel.tsx

@@ -144,9 +144,6 @@ Please retry with an adjusted search pattern or use display_diagram if retries a
         }
     }, [messages]);
 
-    useEffect(() => {
-        console.log("[ChatPanel] Status changed to:", status);
-    }, [status]);
 
     const onFormSubmit = async (e: React.FormEvent<HTMLFormElement>) => {
         e.preventDefault();