This isn't that hard:
How many people per capita from the vaccinated population are hospitalized due to COVID?
How many people per capita from the unvaccinated population are hospitalized due to COVID?
The number is of unvaccinated people requiring vaccination due to COVID is at least 20 times higher, so the vaccines are at least 95% effective at preventing hospitalization.
They did do blind, randomized trials to test these questions before the vaccines were ever approved. That means they set up two groups of equal size, demographic, etc. and give them both shots, half a vaccine and half a placebo. Yet, people participating in the trial do not know which group they are in. They compare the results over the course of months of how both groups fare. That's the best way to test the effectiveness.
The mRNA vaccines were not just 90%+ effective at preventing symptomatic infection, they were even MORE effective at preventing hospitalization and virtually 100% effective in preventing death.
However, now you can see in the population data how effective vaccines are. When you see that 97% or whatever of people hospitalized with COVID are unvaccinated, despite 50% or so of the population being vaccinated, that should tell you something.