Broadcast UserTurnInferenceCompletedFrame on tool calls in filter-incomplete

With ``filter_incomplete_user_turns`` enabled, an LLM that responded to
a user turn by calling a tool (without first emitting a ✓ marker)
never finalized the user turn. ``UserStoppedSpeakingFrame`` stayed
deferred, the assistant aggregator kept ``_user_speaking=True``, and
when ``FunctionCallResultFrame`` arrived its ``not self._user_speaking``
gate dropped the context push — the LLM continuation never ran and
the call hung silently.

Broadcast ``UserTurnInferenceCompletedFrame`` on
``FunctionCallsStartedFrame`` (i.e. the moment the LLM commits to a
tool call, before the function dispatches), gated by a new
``_turn_completion_broadcasted`` flag so the ✓ path and the tool-call
path don't both fire. The flag resets in ``_turn_reset`` alongside
the other per-turn state.

Emitting on the start frame rather than ``LLMFullResponseEndFrame``
also shrinks the race window — ``UserStoppedSpeakingFrame`` (a
``SystemFrame``) has the maximum possible head start over the
``FunctionCallResultFrame`` (``DataFrame``) that follows.

src/pipecat/turns/user_turn_completion_mixin.py

@@ -20,6 +20,7 @@ from loguru import logger
 
 from pipecat.frames.frames import (
     Frame,
+    FunctionCallsStartedFrame,
     InterruptionFrame,
     LLMFullResponseEndFrame,
     LLMMarkerFrame,
@@ -222,6 +223,14 @@ class UserTurnCompletionLLMServiceMixin(FrameProcessor):
         # ensures graceful degradation if the LLM disobeys and outputs additional text.
         self._turn_suppressed = False
         self._turn_complete_found = False  # True when ✓ (COMPLETE) is detected
+        # Set when the LLM made a tool call during this turn. Informational
+        # only — broadcasting is idempotency-gated by
+        # ``_turn_completion_broadcasted``.
+        self._turn_had_function_call = False
+        # True once ``UserTurnInferenceCompletedFrame`` has been broadcast
+        # for this turn. Prevents double-broadcast when ✓ and a tool call
+        # both occur in the same turn.
+        self._turn_completion_broadcasted = False
 
         # Timeout handling
         self._user_turn_completion_config = UserTurnCompletionConfig()
@@ -236,6 +245,27 @@ class UserTurnCompletionLLMServiceMixin(FrameProcessor):
         """
         self._user_turn_completion_config = config
 
+    async def _broadcast_turn_completion(self):
+        """Broadcast ``UserTurnInferenceCompletedFrame`` at most once per turn.
+
+        Called from the two places we know the LLM has committed to a
+        response for the current user turn:
+
+        - the ``✓`` marker is detected in the text stream
+        - a ``FunctionCallsStartedFrame`` is emitted — the LLM committed
+          to a tool call before producing (or instead of) a marker.
+
+        Broadcasting on the tool-call path matters for races: the
+        downstream ``UserStoppedSpeakingFrame`` needs to propagate
+        before the function actually executes and a
+        ``FunctionCallResultFrame`` flows back to the assistant
+        aggregator.
+        """
+        if self._turn_completion_broadcasted:
+            return
+        self._turn_completion_broadcasted = True
+        await self.broadcast_frame(UserTurnInferenceCompletedFrame)
+
     async def _start_incomplete_timeout(self, incomplete_type: Literal["short", "long"]):
         """Start a timeout task for incomplete turn handling.
 
@@ -325,6 +355,8 @@ class UserTurnCompletionLLMServiceMixin(FrameProcessor):
         self._turn_text_buffer = ""
         self._turn_suppressed = False
         self._turn_complete_found = False
+        self._turn_had_function_call = False
+        self._turn_completion_broadcasted = False
 
     async def process_frame(self, frame: Frame, direction: FrameDirection):
         """Process frames, handling turn completion state resets.
@@ -351,7 +383,14 @@ class UserTurnCompletionLLMServiceMixin(FrameProcessor):
             frame: The frame to push downstream.
             direction: The direction of frame flow. Defaults to downstream.
         """
-        if isinstance(frame, LLMFullResponseEndFrame):
+        if isinstance(frame, FunctionCallsStartedFrame):
+            self._turn_had_function_call = True
+            # Broadcast turn completion now, before the function dispatches
+            # — gives ``UserStoppedSpeakingFrame`` maximum time to propagate
+            # so the assistant aggregator's ``_user_speaking`` is False by
+            # the time a ``FunctionCallResultFrame`` arrives.
+            await self._broadcast_turn_completion()
+        elif isinstance(frame, LLMFullResponseEndFrame):
             await self._turn_reset()
 
         await super().push_frame(frame, direction)
@@ -427,7 +466,9 @@ class UserTurnCompletionLLMServiceMixin(FrameProcessor):
             # LLMTurnCompletionUserTurnStopStrategy) can fire
             # `on_user_turn_stopped`. Must fire before the marker so
             # downstream consumers see the signal before the response.
-            await self.broadcast_frame(UserTurnInferenceCompletedFrame)
+            # Idempotent: a tool call earlier in the turn may have
+            # already broadcast.
+            await self._broadcast_turn_completion()
 
             # Push the marker as a sideband signal that the assistant
             # aggregator will prepend to the upcoming aggregated text,