The only "secret" there is a very basic instruction that the model receives, like "summarize current state and upcoming work" before compaction - same model that was just running your inference, with same cache, only server side, with no extra tools or capabilities. Then the fresh context gets the output from that as an encrypted blob + codex then injects up to 64k tokens of previous conversation, the latter part is visible in source code.

There's nothing to gain from this, really. Perhaps they're preparing for something in the future, where they could give the model server-side tools that improves summarization, but right now, it's just a simple prompt.