How important was hand sanitiser during the Covid pandemic? Did it prevent many infections?

Hand sanitizer was not the main event. COVID-19 is a respiratory virus spread mostly through the air, not through surfaces.

The evidence we have on hand sanitizer comes from studies of other germs in hospitals, not from a real-world trial of sanitizer against COVID-19 in the community. One study on Norwalk virus, a stomach bug that spreads through touch, found that alcohol-based hand sanitizer barely worked: it reduced the virus by only about 0.14 log10 (a tiny fraction), while plain soap and water cut it by 0.94 log10 [12]. Another study on C. difficile spores showed that alcohol rubs barely reduced them at all (0.11 to 0.37 log10) and that soap and water was far better [7]. A Vietnamese hospital study did find that alcohol rubs reduced bacteria on hands by about 1.4 log10, which was better than plain soap (0.8 log10) [6]. But bacteria are not a respiratory virus, and a hospital setting is not a pandemic.

The studies that exist were funded by hospital infection-control budgets, not by a manufacturer trying to prove a product works against COVID-19. No study in this set compared people who used hand sanitizer to people who did not and measured who caught COVID-19. That is the study that would answer your question, and it was not done. The public health messaging that made sanitizer seem essential was based on the idea that surfaces matter a lot for COVID-19 transmission. That idea has since been largely walked back by the same agencies that promoted it.

My call: hand sanitizer probably prevented very few COVID-19 infections, because the virus spreads through the air, not mainly through hands. The evidence that it works against respiratory viruses in real-world settings is missing. Confidence: low.