Why? "Summarize in detail what we're doing here and what we have done/learnt so far so another agent can continue" usually works and does not burn the full context length of tokens (uncached) in the new session.
What was your initial problem? I usually work with contexts where they were created, like code session in Cursor / chat in Claude app. When do you have the need to often transfer the history?
You're sending your context to someone's relay in plain text and loading it in plain text.