There are two separate questions: Does an extra booster prevent infection? Does an extra booster reduce hospitalizations and deaths? Seems this study only addressed the first question. But instead of giving a fourth shot based on the OG Covid, seems an updated version based on omicron, delta, and any new variants of concern would be a better idea.
A meta question: how do these studies control for the fact that people who care enough to get a booster are more likely to care proactively about their health?
Lots of good outcomes correlate with caring.