> 15 weeks is rather short. Additionally, it's not really 15 weeks.
You're right. It's the lower bound, based on the duration of the experiment.
There have now been many, many studies all pointing in the same direction. A small selection:
https://www.thelancet.com/journals/lancet/article/PIIS0140-6...
Natural infection protects against Covid (incl. Alpha variant). Adjusted incidence rate ratio for covid infection - 0.159 (84% protection) and symptomatic covid - 0.074 - (93% protection) - 7 month follow up
https://jamanetwork.com/journals/jamainternalmedicine/fullar...
Patients who had 1 PCR positive tests had Hazard ratio 0.06 of further positive PCR - 94% protection - 12 month follow up.
https://academic.oup.com/cid/advance-article/doi/10.1093/cid...
After 1 positive PCR, Protection against any COVID - 81.8%, symptomatic COVID - 84.5% - 6 month follow up - protection increased over time.
https://academic.oup.com/cid/advance-article/doi/10.1093/cid...
seropositive patients had 94% reduction in hazard of testing positive - 8 month follow up
https://www.nejm.org/doi/full/10.1056/NEJMoa2034545
Adjusted risk ratio of covid infection for antibody positive healthcare workers was 0.11 (89% less likely) - 7 month follow up period. All reinfections were asymptomatic.
At this point, claiming that immunity to Covid (even against "the variants") is less than a year is an extraordinary claim. There is no reason, prima facie to presume that the results will be different for vaccines.