But none of this is really Claude Code's internal context, right? It's a summary. I could see using it as an alternative to /compact but not to undo a /clear.

Whatever the internal state is of Claude Code, it's lost as soon as you /clear or close the Terminal window. You can't even experiment with a different prompt and then--if you don't like the prompt--go back to the original conversation, because pressing esc to branch the conversation looses the original branch.