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/caveman.js

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+// Caveman injector: appends a caveman-style instruction into the system message
+// of the final request body, just before it is dispatched to the provider executor.
+// Dispatches by format so it works for both translated and native-passthrough flows.
+
+import { FORMATS } from "../translator/formats.js";
+import { CAVEMAN_PROMPTS } from "./cavemanPrompts.js";
+
+const SEP = "\n\n";
+
+export function injectCaveman(body, format, level) {
+  const prompt = CAVEMAN_PROMPTS[level];
+  if (!body || !prompt) return;
+
+  switch (format) {
+    case FORMATS.CLAUDE:
+      injectClaudeSystem(body, prompt);
+      return;
+    case FORMATS.GEMINI:
+    case FORMATS.GEMINI_CLI:
+    case FORMATS.VERTEX:
+    case FORMATS.ANTIGRAVITY:
+      // Antigravity wraps Gemini shape in body.request → injectGeminiSystem handles it
+      injectGeminiSystem(body, prompt);
+      return;
+    default:
+      // OpenAI and OpenAI-shaped formats (responses/codex/cursor/kiro/ollama)
+      injectMessagesSystem(body, prompt);
+  }
+}
+
+// OpenAI-shaped: messages[] (chat) or input[] (responses) or instructions (responses string)
+function injectMessagesSystem(body, prompt) {
+  // OpenAI Responses API: top-level string field
+  if (typeof body.instructions === "string") {
+    body.instructions = body.instructions
+      ? `${body.instructions}${SEP}${prompt}`
+      : prompt;
+    return;
+  }
+
+  const arr = Array.isArray(body.messages) ? body.messages
+    : Array.isArray(body.input) ? body.input
+    : null;
+  if (!arr) return;
+
+  const idx = arr.findIndex(m => m && (m.role === "system" || m.role === "developer"));
+  if (idx >= 0) {
+    appendToOpenAIMessage(arr[idx], prompt);
+  } else {
+    arr.unshift({ role: "system", content: prompt });
+  }
+}
+
+function appendToOpenAIMessage(msg, prompt) {
+  if (typeof msg.content === "string") {
+    msg.content = `${msg.content}${SEP}${prompt}`;
+  } else if (Array.isArray(msg.content)) {
+    // Responses-style array of parts {type:"input_text"|"text", text}
+    msg.content.push({ type: "input_text", text: prompt });
+  } else {
+    msg.content = prompt;
+  }
+}
+
+// Claude shape: body.system as string | array of {type:"text", text}
+// Insert before the last cache_control block to keep caveman inside the cached prefix.
+function injectClaudeSystem(body, prompt) {
+  if (typeof body.system === "string" && body.system.length > 0) {
+    body.system = `${body.system}${SEP}${prompt}`;
+    return;
+  }
+  if (Array.isArray(body.system)) {
+    const block = { type: "text", text: prompt };
+    let lastCacheIdx = -1;
+    for (let i = body.system.length - 1; i >= 0; i--) {
+      if (body.system[i]?.cache_control) { lastCacheIdx = i; break; }
+    }
+    if (lastCacheIdx >= 0) {
+      body.system.splice(lastCacheIdx, 0, block);
+    } else {
+      body.system.push(block);
+    }
+    return;
+  }
+  body.system = prompt;
+}
+
+// Gemini shape: body.system_instruction | body.systemInstruction | body.request.systemInstruction
+// Each shape: { parts: [{ text }] }
+function injectGeminiSystem(body, prompt) {
+  const target = body.request && typeof body.request === "object" ? body.request : body;
+  const useSnake = Object.prototype.hasOwnProperty.call(target, "system_instruction");
+  const key = useSnake ? "system_instruction" : "systemInstruction";
+  const sys = target[key];
+  if (sys && Array.isArray(sys.parts)) {
+    sys.parts.push({ text: prompt });
+    return;
+  }
+  target[key] = { parts: [{ text: prompt }] };
+}

open-sse/rtk/cavemanPrompts.js

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+// 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(" "),
+};