According to recent studies in the UK, Israel, and US, those who are vaccinated have, on average, a 50% lower risk of developing long COVID.
All of the studies so far have looked at patients from a year ago or more so there are no studies that have looked at the effect of the omicron variant which infected many more people than all previous variants of COVID-19.
Read Evidence grows that vaccines lower the risk of getting long COVID from NPR.