What is the advantage over summarizing previous sessions for the new one?

Or, over continuing the same session and compacting?

You can use it with summaries for sure, but summaries often miss edge cases and long sessions drift. This makes it easier to jump between tasks, come back days later, and reorient without missing something that the summarization or compaction might have gotten rid of. I've often found post-compaction, the memory of even the current session feels so much dumber.