Unless we can get stats for who's eligible or not eligible for the vaccine when they're hospitalized for COVID-19, what can be done with that extra distinction?

Same with age and risk-factor cohorts. We could repeat the probability calculation for each cohort if we could collect those data, but it would probably make the vaccine even more effective: Presumably, more higher-risk people are double/triple/quad vaxxed at this point, so whatever rate they show up to the hospital is higher than what the average healthier person could expect.