Very much agree on your last point.

I think finding out whether or not AI is actually boosting productivity is a problem of measuring productivity period, which at the very least my current company is pretty bad at. For a developer, is their productivity their lines of code produced, hours worked, project tasks completed per unit of time, agile points completed per unit of time, PRs reviewed, PRs submitted? In more human metrics, is it what their coworkers say about them, what leadership says about them, what customers say about them, testers, QA? The amount of bugs they fix, the amount of bugs they don't ship?

Sorry for the ramble, but apply this productivity measurement conundrum to entire corporations and it's no wonder that no productivity boost is being recorded. I'd be surprised if semi-accurate productivity measurements were taken in the first place.