For context, this is a question I answered on Quora

There is no prevention of Long COVID symptoms and the observational studies that find a reduced relative risk of post COVID-19 sequela, which remains a poorly defined construct to this day, are riddled with selection biases, most noticeably sampling and recall bias, since most of them take the form of volunteer survey research or rely on electronic medical records from hospitals, and the healthy vaccinee bias that is likely related to unadjusted confounding variables such as health seeking behavior, gut health/diet and vitamin D serum concentrations. Consider for instance, that black Americans who have a lower COVID-19 vaxx rate than White and asian counterparts also have the highest rate of Vitamin D deficiency especially in the winter time. Despite being highly predictive of SARS-COV-2 infection outcome and risk of infection itself, none of the observational studies purporting to find that the vaxx is associated with a reduced risk of Long COVID symptoms adjust for vitamin D serum levels or gut microbiome health (diet/exercise) as covariates despite the latter being responsible for 70–80% of innate immunity. The largest study to date, with a sample size of 13 million, found that COVID vaxx prior to infection only reduced the risk of long COVID symptoms by 15%. Mind you this is relative risk reduction for people with an elevated risk of Long COVID symptoms from severe infections so it is meaningless to people like myself who only had asymptomatic infection (33–50% of case load) or those with only mild symptoms that can wait out an infection at home (40–50% of case load). Generally, Long COVID studies with fewer selection biases and unadjusted confounding variables are less likely to find any risk reduction at all. A Mayo Clinic retrospective cohort study (n = 41,652) that assessed only attended and professionally diagnosed long COVID symptoms, which eliminates recall and sampling bias found in survey research, found 'no difference in medically-attended and diagnosed post acute sequelae from COVID19 (PASC)between unvaxxed and vaxxed patients who received the full primary series or booster. ' The development of PASC in this study was associated with advance age, female sex, hospitalization for the initial infection, and an increased severity of comorbidities. A matched cohort study, Taquet and colleagues (n = 18,958) confined their data to attended and diagnosed symptoms in electronic health records of pre-omicron infections during a 6 month observation window and only included unvaxxed patients who had received any prior flu shot, which eliminated the recall bias, sampling bias and healthy vaccinee bias present in most long COVID research. After eliminating these three common biases they found that covid vaxx prior to infection was not protective against several documented long COVID symptoms.

I summarized more of this research here:

The COVID Vaxx is Not Associated with Reduced Risk of Long COVID after Infection

Most Long COVID research also only assesses reduced relative risk of post COVID-19 sequela if patients receive the vaxx prior to infection. There is nothing to suggest receiving the vaxx after infection reduces the risk of long COVID symptoms because the short lived anti-receptor binding domain IgG induced immunity from the modRNA transfections do not improve on the much broader and more durable anti-nucleocapsid IgA induced mucosal immunity from infection.

There is no Improvement in Mucosal Immunity

The cluster of symptoms called long COVID are also so poorly defined than they can sometimes be the result of non-COVID related illnesses or disorders. A recent emergency department prospective cohort study spanning per-omicron and omicron variants (n = 6,723) found that 1 in 5 test negative emergency department patients (i.e. no confirmed SARS-2 infection at admission) suffered at least one long COVID symptom providing evidence that the condition is over-diagnosed and the defined symptoms are too ambiguous to accurately pinpoint the prevalence of prolonged COVID19 disease. They also found that ‘vaccination was not associated with less PCC (Post Covid19 Condition Symptoms i.e. Long COVID) in patients with or without SARS CoV-2’.