Codex now lets you tell the LLM tgings in the middle of its thinking without interrupting it, so you can read the thinking traces and tell it to change course if it's going off track.

That just seems like a UI difference. I've always interrupted claude code added a comment and it's continued without much issue. Otherwise if you just type the message is queued for next. There's no real reason to prefer one over the other except it sounds like codex can't queue messages?