feat: Anthropic SDK backend — API key alternative to Claude CLI OAuth

Adds `anthropic_api` model type so users can authenticate with a direct
Anthropic API key instead of (or alongside) the CLI OAuth session.

- model_registry.py: `anthropic_api` type; `save/get/remove_anthropic_api_key()`
  mirroring the Google account pattern; `save_cloud_model()` now picks type
  based on credential type (cli → claude_cli, api_key → anthropic_api);
  `_resolve_model()` merges api_key from the credential entry
- llm_client.py: `_anthropic_api()` backend (AsyncAnthropic SDK); dispatch
  and fallback wiring; usage tracking
- routers/local_llm.py: Anthropic API key management routes
  (POST /settings/local/anthropic-key, /anthropic-key/{id}/remove);
  `anthropic_api` badge and edit-form credential selector
- static/local_llm.html: Anthropic Cloud Provider block now shows API key
  management (add/remove); Add Model → Anthropic tab has credential selector
  (CLI vs API key)
- requirements.txt: enable anthropic>=0.40.0

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

cortex/llm_client.py

@@ -33,15 +33,16 @@ async def cleanup() -> None:
 
 # Map from registry model type → dispatch function key
 _TYPE_TO_BACKEND = {
-    "claude_cli":   "claude",
-    "gemini_cli":   "gemini",
-    "gemini_api":   "gemini",   # gemini_api falls back to CLI in this context
-    "local_openai": "local",
+    "claude_cli":    "claude",
+    "gemini_cli":    "gemini",
+    "gemini_api":    "gemini",        # gemini_api falls back to CLI in this context
+    "local_openai":  "local",
+    "anthropic_api": "anthropic_api",
 }
 
 # Explicit UI toggle values (kept for backward compat)
 _EXPLICIT_BACKENDS = ("claude", "gemini", "local")
-_FALLBACK = {"claude": "gemini", "gemini": "claude", "local": "claude"}
+_FALLBACK = {"claude": "gemini", "gemini": "claude", "local": "claude", "anthropic_api": "claude"}
 
 
 async def complete(
@@ -123,6 +124,8 @@ async def _dispatch(
         return await _gemini(system_prompt, messages)
     if backend == "local":
         return await _local(system_prompt, messages, model_cfg, attachment=attachment)
+    if backend == "anthropic_api":
+        return await _anthropic_api(system_prompt, messages, model_cfg)
     return await _claude(system_prompt, messages, model_cfg)
 
 
@@ -254,6 +257,51 @@ async def _local(
     return text.strip()
 
 
+async def _anthropic_api(system_prompt: str, messages: list[dict], model_cfg: dict | None) -> str:
+    """Direct Anthropic API backend using the anthropic SDK."""
+    try:
+        import anthropic
+    except ImportError:
+        raise RuntimeError("anthropic SDK not installed — run: pip install 'anthropic>=0.40.0'")
+
+    cfg        = model_cfg or {}
+    api_key    = cfg.get("api_key", "")
+    model_name = cfg.get("model_name") or settings.default_model
+
+    if not api_key:
+        raise RuntimeError("No Anthropic API key — add one at /settings/models")
+
+    client = anthropic.AsyncAnthropic(api_key=api_key)
+
+    msgs = [{"role": m["role"], "content": m["content"]} for m in messages]
+    kwargs: dict = {
+        "model":      model_name,
+        "max_tokens": 4096,
+        "messages":   msgs,
+    }
+    if system_prompt:
+        kwargs["system"] = system_prompt
+
+    resp = await client.messages.create(**kwargs)
+
+    text = resp.content[0].text if resp.content else ""
+    if not text.strip():
+        raise RuntimeError("Anthropic API returned an empty response")
+
+    if resp.usage:
+        import usage_tracker
+        from persona import _user
+        asyncio.create_task(usage_tracker.record(
+            username=_user.get(),
+            backend="anthropic_api",
+            model_name=model_name,
+            prompt_tokens=resp.usage.input_tokens,
+            completion_tokens=resp.usage.output_tokens,
+        ))
+
+    return text.strip()
+
+
 async def _gemini(system_prompt: str, messages: list[dict]) -> str:
     # Gemini CLI spawns MCP child processes that keep stdout pipes open after responding.
     # start_new_session=True puts the whole tree in its own process group so