fix: backend toggle not sent to server; add per-message model tag

Fixes:
  - app.js was tracking primaryBackend locally but never included
    model: primaryBackend in the /chat POST body, so the server always
    used settings.primary_backend regardless of what the user clicked.
    Now model: primaryBackend is sent on every chat request.

  - Responses were only annotated when fallback occurred. Now every
    assistant message shows a small model tag at the bottom right.

chat.py:
  - _backend_label() resolves human-readable name:
      claude → "Claude", gemini → "Gemini",
      local → registry label (e.g. "Gemma 4 E4B") or model_name
  - SSE payload now includes backend_label field

app.js:
  - model: primaryBackend added to /chat fetch body
  - After every response, appends .model-tag div with backend_label
  - Fallback shows "⚡ fallback → <label>" in amber; normal is muted
  - Removed separate system message for fallback (tag covers it)

style.css:
  - .model-tag: small muted text, right-aligned, separated by thin line
  - .model-tag.fallback: amber (#f59e0b)

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

cortex/routers/chat.py

@@ -18,6 +18,20 @@ import event_bus
 router = APIRouter()
 
 
+def _backend_label(backend: str, username: str) -> str:
+    """Human-readable label for the model that handled a request."""
+    if backend == "claude":
+        return "Claude"
+    if backend == "gemini":
+        return "Gemini"
+    if backend == "local":
+        cfg = model_registry.get_best_local_model(username)
+        if cfg:
+            return cfg.get("label") or cfg.get("model_name") or "Local"
+        return "Local"
+    return backend.title()
+
+
 class ChatRequest(BaseModel):
     message: str
     session_id: str | None = None
@@ -105,6 +119,7 @@ async def _stream_chat(req: ChatRequest):
                 "response": response_text,
                 "session_id": session_id,
                 "backend": actual_backend,
+                "backend_label": _backend_label(actual_backend, user),
                 "fallback_used": actual_backend != requested,
             }
             yield f"data: {json.dumps(payload)}\n\n"