Some studies find that people who caught Covid despite being vaccinated had lower rates of “long Covid” than the unvaccinated. But other studies found no significant difference. These studies had very different patient sets and parameters (such as what symptoms were tracked and how long the post-acute symptoms lasted).
Vaccines may be able to provide lasting relief in people whose symptoms are caused by vestiges of the virus if the antibodies generated by the vaccines eliminate those remnants.
But in people whose symptoms may be caused by a post-viral response resembling an autoimmune disease, vaccines may help only temporarily, and problems like fatigue could re-emerge. Many of the symptoms are generalized and could come from other causes than Covid.
https://www.nytimes.com/article/long-covid-vaccines.html
Bottom line: Get vaccinated, but also be careful. Covid is still out there and vaccinated people can get long Covid even if their Covid acute phase was too mild to force them into the hospital.
Wendy