I'm not sure that article addresses natural immunity vs vaccine immunity. And it doesn't even conclude that natural immunity is waning, just throws it out there as a possible explanation. (1 of 4 possible explanations). Even then calls that explanation "unlikely to fully explain resurgence". Also, says later, "if resurgence in Manaus is due to waning of protective immunity, then similar resurgence scenarios should be expected in other locations", but we have not seen that here in the US, nor in Europe. etc.
Moreover they cite the NEJM study from 2020 suggesting 6 mo immunity and then talk about how in Manaus the period was 7-8 months. But a subsequent June 2021 study shows at least 10 month immunity.
https://www.thelancet.com/journals/lanhl/article/PIIS2666-7568(21)00093-3/fulltext