Carmack has a point, we should focus on the problem we're solving and the value we're delivering. It can be hard for programmers to get this sometimes, but it will make you much better at your job now, it's not just about future-proofing. That said, I love technology and delivering it through code, so I would struggle on a personal level in this future unless there were interesting technical roles left to do. I have no interest in being a product person. I'm fundamentally motivated by a passion for code and tech.
As for when this fully automated future arrives, I don't know, but I don't think LLMs get you there. More and more boilerplate code, and even novel code, might get written by things like Codex. However, all the messy details of real world systems solving fairly intractable problems need something more akin to, if not AGI, then another type of AI. I might be wrong, I just don't feel that threatened by ChatGPT / Copilot based on what I've seen. It's an amazing technology but weirdly underwhelming for my job. Copilot etc will change things, but replace us? No.
Of course, something else may be just around the corner so I'm not complacent.