My understanding is that a fourth booster doesn't seem to prevent breakthrough infections (which are very common with Omicron), but it does seem to reduce sever

My understanding is that a fourth booster doesn't seem to prevent breakthrough infections (which are very common with Omicron), but it does seem to reduce severity and hospitalizations (which are very uncommon with Omicron). Maybe it reduces the chance of a breakthrough but it's still common. This is what the third booster does and probably also what being vaccinated closer to infection date does. This is exactly what happens when you have more antibodies.