They sampled people who were getting tested for COVID, and divided the samples into vaccinated-with-breakthrough-cases-who-got-tested and unvaccinated-and-sick-who-got-tested.

This completely fails to account for people who are vaccinated, and don't have breakthrough cases, which is the overwhelming majority of vaccinated individuals.

Because of the incredible sampling bias in the study [1], the conclusions that it makes are significantly less extraordinary than your claims.

Just because someone somewhere runs a study that compares 50 dead-in-car-crash people who were wearing seat belts, and 50 dead people who weren't wearing seat belts, you can't conclude that wearing a seatbelt does not reduce your risk of death or injury.