People are misusing this Nature study, both to push their 'anti-narrative' message, and to push a low resolution 'anti-anti-narrative' narrative.
As shown in Table 2, unvaccinated people with a previous infection were indeed counted as 'fully vaccinated'. But the authors acknowledge this, explain why, and claim that segregating the cohorts does not change their results nor their conclusions.
People who take science seriously continue to engage, criticise and explore on this point, and that's healthy.
But the anti-narrative people have a strong argument because this collapsing of cohorts into 'fully vaccinated' - even if not deliberately misleading - is being used in misleading ways. Those quoting this Nature study are using it to bolster the tired 'pandemic of the unvaccinated' narrative when that is not the conclusion at all.
The study actually makes the conclusion that the rapid spread of Omicron compared to Delta was due to 'immune evasiveness' or what previous Discernable guest Geert Vanden Bossche warned about: 'immune escape', and much less due to any increased transmissibility of the Omicron strain itself.
It also notes in the Discussion section that Omicron is 2.4-3.2 times more transmissible than Delta among the vaccinated, 'but similar in transmissibility among unvaccinated'.
You can read the study for yourself at: https://www.nature.com/articles/s41467-022-33328-3