Wrong. The study cited in [47] clearly talks about the therapies from AstraZeneca/Oxford, Moderna and Pfizer/BioNTech
https://www.medrxiv.org/content/10.1101/2021.01.27.20240309v...
https://www.medrxiv.org/content/10.1101/2021.01.27.20240309v...
47 in link above is a study of the cruise ship, not what you think.
If you meant the actual link above, it clearly states vaccines give immunity but it might be waning, i.e: won't last, same as natural immunity
Best of luck, thought I might help with your logic, but I admit defeat there.