feat: record streaming token usage in TrackedLLMClient.stream_chat

Implement manual generator driving using next()/StopIteration to capture
the return value (trailing usage dict) from inner stream_chat() implementations,
enabling token tracking for streaming LLM calls.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

backend/app/services/llm/tracked_client.py

@@ -56,18 +56,24 @@ class TrackedLLMClient:
         return response
 
     def stream_chat(self, messages: List[Dict[str, str]], *args: Any, **kwargs: Any):
-        """Delegate to the wrapped client's stream_chat(), recording call outcome only.
+        """Delegate to the wrapped client's stream_chat(), recording call outcome and usage.
 
-        Token usage is NOT recorded here: none of the current provider
-        stream_chat() implementations parse a trailing usage chunk from the
-        gateway (see the design doc's Known Limitations), so accumulating a
-        token count here would silently be wrong. Only call success/failure
-        and latency are tracked for streaming calls.
+        Drives the inner generator manually (instead of a plain `for` loop) so
+        it can capture the generator's return value via StopIteration.value —
+        the trailing token-usage dict the inner client captures from a
+        stream_options.include_usage chunk, if the gateway sent one.
         """
         start = time.time()
         error: Optional[str] = None
+        usage: Optional[Dict[str, int]] = None
+        gen = self._inner.stream_chat(messages, *args, **kwargs)
         try:
-            for chunk in self._inner.stream_chat(messages, *args, **kwargs):
+            while True:
+                try:
+                    chunk = next(gen)
+                except StopIteration as stop:
+                    usage = stop.value
+                    break
                 yield chunk
         except Exception as exc:  # noqa: BLE001 - report, then re-raise unchanged
             error = str(exc)
@@ -77,6 +83,7 @@ class TrackedLLMClient:
                 provider=self._inner.config.provider.value,
                 model=self._inner.config.model,
                 success=error is None,
+                usage=usage,
                 latency_ms=int((time.time() - start) * 1000),
                 error=error,
             )