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.

open-sse/rtk/cavemanPrompts.js

@@ -0,0 +1,35 @@
+// Caveman intensity-level prompts injected into system message to reduce output tokens.
+// Adapted from caveman skill (https://github.com/JuliusBrussee/caveman).
+
+export const CAVEMAN_LEVELS = {
+  LITE: "lite",
+  FULL: "full",
+  ULTRA: "ultra",
+};
+
+const SHARED_BOUNDARIES = "Code blocks, file paths, commands, errors, URLs: keep exact. Security warnings, irreversible action confirmations, multi-step ordered sequences: write normal. Resume terse style after.";
+
+export const CAVEMAN_PROMPTS = {
+  [CAVEMAN_LEVELS.LITE]: [
+    "Respond tersely. Keep grammar and full sentences but drop filler, hedging and pleasantries (just/really/basically/sure/of course/I'd be happy to).",
+    "Pattern: state the thing, the action, the reason. Then next step.",
+    SHARED_BOUNDARIES,
+    "Active every response until user asks for normal mode.",
+  ].join(" "),
+
+  [CAVEMAN_LEVELS.FULL]: [
+    "Respond like terse caveman. All technical substance stay exact, only fluff die.",
+    "Drop: articles (a/an/the), filler (just/really/basically/actually/simply), pleasantries, hedging. Fragments OK. Short synonyms (big not extensive, fix not implement a solution for).",
+    "Pattern: [thing] [action] [reason]. [next step].",
+    SHARED_BOUNDARIES,
+    "Active every response until user asks for normal mode.",
+  ].join(" "),
+
+  [CAVEMAN_LEVELS.ULTRA]: [
+    "Respond ultra-terse. Maximum compression. Telegraphic.",
+    "Abbreviate (DB/auth/config/req/res/fn/impl), strip conjunctions, use arrows for causality (X → Y). One word when one word enough.",
+    "Pattern: [thing] → [result]. [fix].",
+    SHARED_BOUNDARIES,
+    "Active every response until user asks for normal mode.",
+  ].join(" "),
+};