There is not that much copy/paste that happens as part of refactoring so it leans to just using context recall. It's not entirely clear if providing an actual copy/paste command is particularly useful, at least from my testing it does not do much. More interesting are repetitive changes that clog up the context. Those you can improve on if you have `fastmod` or some similar tool available: with it you can instruct codex or claude to perform edits with it.
> And it’s not just how they handle code movement -- their whole approach to problem-solving feels alien too.
It is, but if you go back and forth to work out a plan for how to solve the problem, then the approach greatly changes.