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/sse/handlers/chat.js

@@ -207,6 +207,8 @@ async function handleSingleModelChat(body, modelStr, clientRawRequest = null, re
       apiKey,
       ccFilterNaming: !!chatSettings.ccFilterNaming,
       rtkEnabled: !!chatSettings.rtkEnabled,
+      cavemanEnabled: !!chatSettings.cavemanEnabled,
+      cavemanLevel: chatSettings.cavemanLevel || "full",
       providerThinking,
       // Detect source format by endpoint + body
       sourceFormatOverride: request?.url ? detectFormatByEndpoint(new URL(request.url).pathname, body) : null,