Fix context summarization failing with mid-conversation system messages

Only treat messages[0] as the initial system prompt when determining the
summarization range. Previously, the code scanned the entire context for
the first system-role message, which caused failures when the only system
message was a mid-conversation injection (e.g. "The user has been quiet").
In that case summary_start exceeded summary_end, producing an empty range
and "No messages to summarize" errors.

Fixes #4286

src/pipecat/processors/aggregators/llm_context_summarizer.py

@@ -429,18 +429,17 @@ class LLMContextSummarizer(BaseObject):
         config = self._auto_config.summary_config
         messages = self._context.messages
 
-        # Find the first system message to preserve. LLMSpecificMessage instances are excluded
-        # because they are not dict-like and never represent a system message; they hold
-        # service-specific metadata (e.g. thinking blocks) that is always paired with a
-        # standard message.
-        first_system_msg = next(
-            (
-                msg
-                for msg in messages
-                if not isinstance(msg, LLMSpecificMessage) and msg.get("role") == "system"
-            ),
-            None,
-        )
+        # Preserve the first message if it is a system message (initial system prompt).
+        # Only messages[0] is treated as the system preamble — system messages at
+        # other positions are mid-conversation injections and are not preserved
+        # separately (they will be part of the summary or the recent messages).
+        first_system_msg = None
+        if (
+            messages
+            and not isinstance(messages[0], LLMSpecificMessage)
+            and messages[0].get("role") == "system"
+        ):
+            first_system_msg = messages[0]
 
         # Get recent messages to keep
         recent_messages = messages[last_summarized_index + 1 :]

src/pipecat/utils/context/llm_context_summarization.py

@@ -522,25 +522,19 @@ class LLMContextSummarizationUtil:
         if len(messages) <= min_messages_to_keep:
             return LLMMessagesToSummarize(messages=[], last_summarized_index=-1)
 
-        # Find first system message index. LLMSpecificMessage instances are excluded because
-        # they are not dict-like and never represent a system message; they hold
-        # service-specific metadata (e.g. thinking blocks) that is always paired with a
-        # standard message.
-        first_system_index = next(
-            (
-                i
-                for i, msg in enumerate(messages)
-                if not isinstance(msg, LLMSpecificMessage) and msg.get("role") == "system"
-            ),
-            -1,
+        # Check if the first message is a system message (initial system prompt).
+        # Only messages[0] is treated as the system message to preserve — system
+        # messages at other positions are mid-conversation injections and should be
+        # included in the summarization range.
+        first_msg = messages[0] if messages else None
+        first_is_system = (
+            first_msg is not None
+            and not isinstance(first_msg, LLMSpecificMessage)
+            and first_msg.get("role") == "system"
         )
 
-        # Messages to summarize are between first system and recent messages
-        # We exclude the first system message itself
-        if first_system_index >= 0:
-            summary_start = first_system_index + 1
-        else:
-            summary_start = 0
+        # Start summarization after the initial system message if present
+        summary_start = 1 if first_is_system else 0
 
         # Get messages to keep (last N messages)
         summary_end = len(messages) - min_messages_to_keep