A cesarean is major surgery, and the risks are real but not the same for everyone
Serious harm is uncommon. It is not zero.
Comparing cesarean and vaginal birth honestly is hard, because women who need a cesarean are usually sicker to begin with. This is called confounding by indication, and it makes raw comparisons overstate the danger of the operation itself.
Two studies were designed specifically to reduce that problem. A Canadian study of low-risk women found severe complications in 27.3 per 1,000 planned cesareans compared with 9.0 per 1,000 planned vaginal births, with no significant difference in death. A French study of 182,300 deliveries, using a statistical method designed to compare women who were otherwise similar to each other, found roughly a 1.8-fold higher risk of severe complications with cesarean, and the excess was much larger in women aged 35 and older. That study reports only a relative figure and gives no absolute rates of its own, so the Canadian numbers above are the ones to hold in mind for scale.