Write messages to backend storage before offloading.
Appends messages as a timestamped markdown section to the conversation
history file, matching the SummarizationMiddleware offload pattern.
Filters out prior summary messages using the middleware's
_filter_summary_messages to avoid storing summaries-of-summaries.
Messages to offload.
SummarizationMiddleware instance for filtering.
Thread identifier used to derive the storage path.
Backend to persist conversation history to.
