The science is actually far from settled on this. There is no randomized controlled trial of vaccinating the previously infected.
And while this pre-print [0] establishes that natural immunity is far stronger than vaccine-only immunity, the result is not conclusive for natural immunity + vaccine:
“Individuals who were previously infected with SARS-CoV-2 seem to gain additional protection from a subsequent single-dose vaccine regimen. Though this finding corresponds to previous reports, we could not demonstrate significance in our cohort.”
If you are talking about significance, you are taking that quote completely out of context. There's a reason we give people two doses, but this study only looked at one dose and still found an effect. It didn't reach the technical level of "significance," but that does not mean it is not there. If your saying it supports me, that's not enough evidence. Here's a different study that looked at both doses and found you were twice as likely to be reinfected if you didn't get the vaccine. [0]
So, what did we learn? The science seems confident that getting the full regimen of the vaccine is a good idea because it lowers you chance of getting reinfected and the likelihood of side effects are extremely small.
And while this pre-print [0] establishes that natural immunity is far stronger than vaccine-only immunity, the result is not conclusive for natural immunity + vaccine:
“Individuals who were previously infected with SARS-CoV-2 seem to gain additional protection from a subsequent single-dose vaccine regimen. Though this finding corresponds to previous reports, we could not demonstrate significance in our cohort.”
[0] https://www.medrxiv.org/content/10.1101/2021.08.24.21262415v...