Global electrical production in 2022 was ~30,000 TWh.[1]
If we over-estimate that a hyperscale data-center will consume about 100 MW of power, per year that would be around 876 GWh.[2]
Let's overestimate again and say that 1,000 new data centers spring up in a year, every year they would consume 876 TWh.
Which, is 2.92% of total electricity production. Which given the fact that I overestimated the energy consumption by more than an order of magnitude, I would say the term "rounding error" is accurate.
I think the main limiting factor in the near term is going to be chip production capacity. The fabs take so long to spin up, it's going to be a while before we can even consider "electricity production" being a limiting factor.
[1] https://yearbook.enerdata.net/electricity/world-electricity-... [2] https://cc-techgroup.com/data-center-energy-consumption/