All of them.

Not programming, but:

Requirements gathering. System Analysis. System Design. Engineering.

Will all matter the same as they do now.

It's tough to say because we definitely have created an exoskeleton with AI. We would need to tell a society with ubiquitous exoskeletons to mindfully exercise their body so it does not atrophy. The exercise you would get hiking will never translate to core body strength with the exoskeleton on. Likewise, core body strength would only have ambiguous value since everything would be done with an exoskeleton regardless since it's simply better. For programming specifically, you can already see it with Leetcode. Which of the Leetcode problems really matter and why for most work? Few for most us, but whoever is deciding what is important will decide what it is important. Google for example decides which Leetcode problems are important and they will decide in the future in the same way. It will have nothing to do with the reality of the day to day.

This is a very long-winded way of saying gatekeepers gonna gatekeep.

Debugging. No matter what’s created and how it’s created it will have to be debugged.

Probably software design and architecture.

Anyone can do programming. That's not really that impressive.

Writing/organizing/evolving software so it scales along with the organization (note: not speaking about performance here) is super important.

How will the software be built/maintained/deployed when there are dozens of orgs, each with dozens of teams and sub-teams?

It's going to be more about engineering. We don't need to know how transistors work to make a website. But moving forward, you do want to know patterns like repositories. You want to know terms like "decompose a conditional" - most programmers already decompose conditionals, they just don't know what it's called because we never had to use the term. AI knows all the term, use the language. AI is also amazing with stuff like DDD, and I find that when working on some creative work, I might ask it to just break down a concept into ubiquitous language and such.

And let's say AI does all the programming for us, but engineers are there to know what can be programmed and what couldn't. Engineers are there to prevent business from trying to make flying submarines.

Basically engineers are the girl in front of the computer who can answer this question: https://xkcd.com/1425/

All of them.

Look what mattered 10 years ago, reflect on that, and draw your own conclusions.

Sprinklers. Have you ever tried to program the timers on one? They're hell!

But after the AIpocalypse, it's only the not-yet-sentient sprinklers that will still be willing to water our few remaining crops and feed us.