I'm fairly sure that Claude adds a note where it can find the original transcript after compactation (somewhat recently).

Fwiw I built a little CLI that could help with this, https://github.com/martinalderson/claude-log-cli. It allows Claude to search its own logs very efficiently. So I'm sure you could add something like "if the session is continued from a previous one, use claude-log cli to find users original prompt with claude-log" which would pull it out very efficiently. I built it to enable self improving claude.md files (link to the blog in the GitHub) but it's so useful for many tasks.