Herd immunity is a function of transmission not individual infection. Faster and stronger immune responses reduce the number of viruses produced inside someone over an infection. That directly means they are less likely to infect other people.

Herd immunity is effectively a function of how infections something is. 1 case leading to 2 cases on average means you need to cut transmission in 50%. 1 case leading to 10 cases and you need to block 90% of new cases.

Critically this means vaccinated people can still be infectious as long as they infect less than 1 person on average you can reach herd immunity.