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/api/chat/route.js

@@ -8,7 +8,6 @@ async function ensureInitialized() {
   if (!initialized) {
     await initTranslators();
     initialized = true;
-    console.log("[SSE] Translators initialized");
   }
 }
 

src/app/api/v1/chat/completions/route.js

@@ -11,7 +11,6 @@ async function ensureInitialized() {
   if (!initialized) {
     await initTranslators();
     initialized = true;
-    console.log("[SSE] Translators initialized");
   }
 }
 

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

@@ -10,7 +10,6 @@ async function ensureInitialized() {
   if (!initialized) {
     await initTranslators();
     initialized = true;
-    console.log("[SSE] Translators initialized for /v1/messages");
   }
 }
 

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");
   }
 }
 

src/app/api/v1beta/models/[...path]/route.js

@@ -10,7 +10,6 @@ async function ensureInitialized() {
   if (!initialized) {
     await initTranslators();
     initialized = true;
-    console.log("[SSE] Translators initialized for /v1beta/models");
   }
 }