You let them play out. Shift-left was similar to this and ultimately ended in part disaster, part non-accomplishment, and part success. Some percentage of the industry walked away from shift-left greatly more capable than the rest, a larger chunk left the industry entirely, and some people never changed. The same thing will likely happen here. We'll learn a lot of lessons, the Overton window will shift, the world will be different, and it will move on. We'll have new problems and topics to deal with as AI and how to use it shifts away from being a primary topic.
Edit: I've googled it and I can't find anything relevant. I've been working in software for 20+ years and read a myriad things and it's the first time I hear about it...
I also believe coding isn't going to disappear, but AI skeptics have been mostly doing a combination of moving the goalposts and straight up denial over the last few years.
I haven't seen a lot of goalpost moving on either side; the closest I've seen is from the most hyperbolic of AI supporters, who are keeping the timeline to supposed AGI or AI superintelligence or whatnot a fairly consistent X months from now (which isn't really goalpost-moving).
Over the course of about 2 years, the general consensus has shifted from "it's a fun curiosity" to "it's just better stackoverflow" to "some people say it's good" to "well it can do some of my job, but not most of it". I think for a lot of people, it has already crossed into "it can do most of my job, but not all of it" territory.
So unless we have finally reached the mythical plateau, if you just go by the trend, in about a year most people will be in the "it can do most of my job but not all" territory, and a year or two after that most people will be facing a tool that can do anything they can do. And perhaps if you factor in optimisation strategies like the Karpathy loop, a tool that can do everything but better.
Upper managment might be proven right.
I would do the initial research/planning/etc. mostly honestly and fairly. I'd find the positives, build a real roadmap and lead meetings where I'd work to get people onboard.
Then I'd find the fatal flaw. "Even though I'm very excited about this, as you know, dear leadership, I have to be realistic that in order to do this, we'd need many more resources than the initial plan because of these devastating unexpected things I have discovered! Drat!"
I would then propose options. Usually three, which are: Continue with the full scope but expand the resources (knowing full well that the additional resources required cannot be spared), drastically cut scope and proceed, or shelve it until some specific thing changes. You want to give the specific thing because that makes them feel like there's a good, concrete reason to wait and you're not just punting for vague, hand-wavy reasons.
Then the thing that we were waiting on happens, and I forget to mention it. Leadership's excited about something else by that point anyway, so we never revisit dumb project again.
Some specific thoughts for you:
1. Treat their arguments seriously. If they're handwaving your arguments away, don't respond by handwaving their arguments away, even if you think they're dumb. Even if they don't fully grasp what they're talking about, you can at least concede that agents and models will improve and that will help with some issues in the future.
2. Having conceded that, they're now more likely to listen to you when you tell them that while it's definitely important to think about a future where agents are better, you've got to deal with the codebase right now.
3. Put the problems in terms they'll understand. They see the agent that wrote this feature really quickly, which is good. You need to pull up the tickets that the senior developers on the team had to spend time on to fix the code that the agent wrote. Give the tradeoff - what new features were those developers not working on because they were spending time here?
4. This all works better if you can position yourself as the AI expert. I'd try to pitch a project of creating internal evals for the stuff that matters in your org to try with new models when they come out. If you've volunteered to take something like that on and can give them the honest take that GPT-5.5 is good at X but terrible at Y, they're probably going to listen to that much more than if they feel like you're reflexively against AI.
Where the tech argument doesn't apply to upper management, business practices, the need to "not be left behind" and leap at anything that promises reducing headcount without reducing revenue, money talks. As long as it's possible to slop something together, charge for it, and profit, slop will win.