Enhance chat handling and introduce Caveman feature

- Refactored handleChatCore to include Caveman functionality, allowing for terse-style system prompts to reduce output token usage.
- Updated APIPageClient to manage Caveman settings, including enabling/disabling and selecting compression levels.
- Adjusted AntigravityExecutor to consolidate function declarations for compatibility with Gemini.
- Removed unnecessary console logs during translator initialization across multiple routes.

src/app/api/v1/responses/route.js

@@ -7,7 +7,6 @@ async function ensureInitialized() {
   if (!initialized) {
     await initTranslators();
     initialized = true;
-    console.log("[SSE] Translators initialized for /v1/responses");
   }
 }