There are studies demonstrating reduced long covid symptoms in those who were vaccinated then infected vs those who were unvaccinated then infected. The first study looks at exactly what Mofro mentions:
https://www.medrxiv.org/content/10.1....05.22268800v2
Vaccination with at least two doses of COVID-19 vaccine was associated with a substantial decrease in reporting the most common post-acute COVID-19 symptoms, bringing it back to baseline. Our results suggest that, in addition to reducing the risk of acute illness, COVID-19 vaccination may have a protective effect against long COVID.
https://www.thelancet.com/journals/l...460-6/fulltext
Vaccination (compared with no vaccination) was associated with reduced odds of ... long-duration (≥28 days) symptoms following the second dose. Almost all symptoms were reported less frequently in infected vaccinated individuals than in infected unvaccinated individuals
NIH reviewed 6 studies and came to the same conclusions that vaccination reduces Long COVID risk
https://ukhsa.koha-ptfs.co.uk/cgi-bi...5ad4f72ae0dfff