So its basically (a plan + a bunch of file reads + a first edit) injected into the context of a cheap model so the cheap model does not feel like it has to re-read the files and just continues executing and editing?

Yes this is correct. It essentially biases the cheaper model into procedural action grounded by the frontier model. To put it mode generally, it injects the cheap model context with more useful information, where it might not need to read all the files again.