If you're working with text and you have some regularities in your workflow, you can gain some productivity points from current technology. In time most industries will have these regularities, similar to workflow improvements after the introduction of computer.
But I also doubt if it will have that much effect. In general we have diminishing returns from these kind of technology, telegraph's effect on the world was larger than the computer, computers were more valuable than WWW and search engines have smaller effect than WWW. AI may be big, but could it be bigger than search or e-commerce? I doubt it.
If computers really had little impact on productivity then things like the Cloudstrike outage would be barely noticed, instead of causing instant mass disruption worldwide due to sudden productivity loss. It would also imply that everyone, everywhere, in every industry, is an idiot who adopted computers despite not getting much return. That isn't plausible, so it's more likely that there's a problem with data.
In particular, note that productivity growth of 1% is compounding. Each year you need bigger and bigger upgrades to sustain that 1% growth.
More likely the productivity growth was captured by the average poor in all the free programs we get today. Free google, free youtube, free porn, free wikipedia, free games, free...
That is a massive amount of content and products you consume today that just aren't accurately valued by GDP, and thus not captured by productivity measurements. The companies providing those services makes money in other ways, sure, but that value isn't even close to the amount of money it would have costed to buy that much products for consumers in the old economy.
Just take the amount of porn consumed by the average teenager today, that would have costed a fortune 30 years ago while today he got it for free.
But I also doubt if it will have that much effect. In general we have diminishing returns from these kind of technology, telegraph's effect on the world was larger than the computer, computers were more valuable than WWW and search engines have smaller effect than WWW. AI may be big, but could it be bigger than search or e-commerce? I doubt it.