I don't understand this study. Why not compare the hospitalization/fatality rates between _current_ omicron/delta infections between similar cohorts?

Comparing to an earlier wave is hopelessly confounded on prior infections in the intervening time and similarly, on the most susceptible having already been killed off.

Maybe they did what I'm suggesting and its mostly just bad reporting?

edit from the summary :-/ :

Vaccine effectiveness:

    The two-dose Pfizer-BioNTech vaccination provides 70% protection against severe complications of COVID-19 requiring hospitalisation, and 33% protection against COVID-19 infection, during the current Omicron wave. 

    Reinfection risk: For individuals who have had COVID-19 previously, the risk of reinfection with Omicron is significantly higher, relative to prior variants.

    Severity: The risk of hospital admission among adults diagnosed with COVID-19 is 29% lower for the Omicron variant infection compared to infections involving the D614G mutation in South Africa’s first wave in mid-2020, after adjusting for vaccination status

    Children: Despite very low absolute incidence, preliminary data suggests that children have a 20% higher risk of hospital admission in Omicron-led fourth wave in South Africa, relative to the D614G-led first wave.