For a rough but well-sourced overview, see Wikipedia: https://en.wikipedia.org/wiki/Threshold_theorem
For a review paper on surface codes, see A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, “Surface codes: Towards practical large-scale quantum computation,” Phys. Rev. A, vol. 86, no. 3, p. 032324, Sep. 2012, doi: 10.1103/PhysRevA.86.032324.
The claim about this is that correlated errors will lead to an "error floor", a certain size of error correction past which exponential reduction in errors no longer applies, due to a certain frequency of correlated errors. See figure 3a of the arxiv version of the paper: https://arxiv.org/abs/2408.13687
Not sure why you would say that? This sort of exponential suppression of errors is exactly how quantum error correction works and why we think quantum computing is viable. Source: have worked on quantum error correction for a couple of decades. Disclosure: I work on the team that did this experiment. More reading: lecture notes from back in the day explaining this exponential suppression https://courses.cs.washington.edu/courses/cse599d/06wi/lectu...
That's an EXTRAORDINARY claim and one that contradicts the experience of pretty much all other research and development in quantum error correction over the course of the history of quantum computing.