fix: surface TTSSpeakFrame greetings in on_assistant_turn_stopped

Two issues were causing TTSSpeakFrame(append_to_context=True) greetings to
silently lose their trailing words and never fire on_assistant_turn_stopped:

- LLMAssistantPushAggregationFrame was emitted without a PTS, so the
  transport routed it through the audio (sync) queue while word-level
  TTSTextFrames travel through the clock queue. The aggregation could reach
  the assistant aggregator before the final words, leaving them orphaned
  in the buffer. Stamp the frame with `_word_last_pts + 1` when there are
  word timestamps so it can't overtake them.

- The aggregator's LLMAssistantPushAggregationFrame handler called
  push_aggregation() directly, bypassing _trigger_assistant_turn_stopped.
  For TTS-only flows there is no LLMFullResponseStartFrame, so the turn
  start timestamp was never set and on_assistant_turn_stopped never fired.
  Open a turn (if needed) and trigger stopped from the handler.

Fixes #4264.

src/pipecat/processors/aggregators/llm_response_universal.py

@@ -927,7 +927,7 @@ class LLMAssistantAggregator(LLMContextAggregator):
             await self._handle_end_or_cancel(frame)
             await self.push_frame(frame, direction)
         elif isinstance(frame, LLMAssistantPushAggregationFrame):
-            await self.push_aggregation()
+            await self._handle_push_aggregation()
         elif isinstance(frame, LLMFullResponseStartFrame):
             await self._handle_llm_start(frame)
         elif isinstance(frame, LLMFullResponseEndFrame):
@@ -1309,6 +1309,17 @@ class LLMAssistantAggregator(LLMContextAggregator):
     async def _handle_llm_end(self, _: LLMFullResponseEndFrame):
         await self._trigger_assistant_turn_stopped()
 
+    async def _handle_push_aggregation(self):
+        # LLMAssistantPushAggregationFrame is emitted by TTSService at the end
+        # of a TTSSpeakFrame-driven utterance (no surrounding LLM response
+        # cycle), so no LLMFullResponseStartFrame ever set the turn-start
+        # timestamp. Open a turn now so on_assistant_turn_stopped fires for the
+        # greeting text the same way it did before LLMAssistantPushAggregationFrame
+        # was introduced.
+        if not self._assistant_turn_start_timestamp:
+            await self._trigger_assistant_turn_started()
+        await self._trigger_assistant_turn_stopped()
+
     async def _handle_text(self, frame: TextFrame):
         # Skip TextFrame types not intended to build the assistant context
         if isinstance(frame, (TranscriptionFrame, TranslationFrame, InterimTranscriptionFrame)):

src/pipecat/services/tts_service.py

@@ -771,7 +771,17 @@ class TTSService(AIService):
         if isinstance(frame, TTSStoppedFrame) and frame.context_id:
             if frame.context_id in self._tts_contexts:
                 if self._tts_contexts[frame.context_id].push_assistant_aggregation:
-                    await self.push_frame(LLMAssistantPushAggregationFrame())
+                    aggregation_frame = LLMAssistantPushAggregationFrame()
+                    # When word-level TTSTextFrames are routed through the
+                    # transport's clock queue (PTS-based), the aggregation frame
+                    # would otherwise take the audio (sync) queue path and
+                    # could overtake the final word frames. Stamping it with a
+                    # PTS just past the last word forces it through the clock
+                    # queue too, so the assistant aggregator sees every word
+                    # before flushing.
+                    if self._word_last_pts:
+                        aggregation_frame.pts = self._word_last_pts + 1
+                    await self.push_frame(aggregation_frame)
                 logger.debug(f"{self} cleaning up TTS context {frame.context_id}")
                 del self._tts_contexts[frame.context_id]