feat: OpenAI-compatible orchestrator + backend auto-routing

- openai_orchestrator.py — new ReAct tool loop engine for any
  OpenAI-compatible endpoint (OpenRouter, Open WebUI, Ollama, LiteLLM);
  model handles both tool loop and final response, no Claude handoff needed
- tools/__init__.py — auto-derive OpenAI JSON Schema from existing Gemini
  FunctionDeclarations so tool definitions have a single source of truth
- routers/orchestrator.py — route to openai_orchestrator when model registry
  "orchestrator" role resolves to a local_openai type host
- routers/chat.py — pass role to _backend_label(); fix fallback_used logic
  (only meaningful for explicit backend overrides, not auto-routing)
- static/app.js — add null/"auto" to backend cycle; fetch local model hint
  without overriding the auto default on page load
- model_registry.py — _normalize() back-fills host_type on old registry files
- requirements.txt — add openai>=1.0.0
- ARCH__BACKENDS.md — document OpenAI-compat backend and routing logic

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

cortex/tools/__init__.py

@@ -551,3 +551,61 @@ async def call_tool(name: str, args: dict) -> str:
     if fn is None:
         return f"Unknown tool: {name}"
     return await fn(**args)
+
+
+# ---------------------------------------------------------------------------
+# OpenAI JSON Schema format — auto-derived from the Gemini declarations above
+# so there is a single source of truth for tool definitions.
+# ---------------------------------------------------------------------------
+
+_GEMINI_TYPE_TO_JSON = {
+    "OBJECT":  "object",
+    "STRING":  "string",
+    "INTEGER": "integer",
+    "NUMBER":  "number",
+    "BOOLEAN": "boolean",
+    "ARRAY":   "array",
+}
+
+
+def _schema_to_json(schema) -> dict:
+    """Recursively convert a Gemini types.Schema to a JSON Schema dict."""
+    type_name = getattr(getattr(schema, "type", None), "name", "STRING")
+    result: dict = {"type": _GEMINI_TYPE_TO_JSON.get(type_name, "string")}
+
+    if getattr(schema, "description", None):
+        result["description"] = schema.description
+
+    props = getattr(schema, "properties", None) or {}
+    if result["type"] == "object":
+        result["properties"] = {k: _schema_to_json(v) for k, v in props.items()}
+
+    req = getattr(schema, "required", None)
+    if req:
+        result["required"] = list(req)
+
+    return result
+
+
+def _build_openai_tools() -> list[dict]:
+    """Convert TOOL_DECLARATIONS (Gemini format) to OpenAI tool schemas."""
+    out = []
+    for decl in TOOL_DECLARATIONS[0].function_declarations:
+        params = (
+            _schema_to_json(decl.parameters)
+            if decl.parameters
+            else {"type": "object", "properties": {}}
+        )
+        out.append({
+            "type": "function",
+            "function": {
+                "name": decl.name,
+                "description": decl.description or "",
+                "parameters": params,
+            },
+        })
+    return out
+
+
+# OpenAI-format tool list — pass to client.chat.completions.create(tools=...)
+OPENAI_TOOL_SCHEMAS: list[dict] = _build_openai_tools()