I did see studies with control groups that suggested that the vaccine did reduce viral load by 30% (when effective to the correct strain), and that could lead to less hospitalizations (because you'll be theoretically less sick), but I don't think there's any clear evidence that it did.
I still haven't seen untainted data that proves the vaccines reduce hospitalization.
I suppose we'll never know because they didn't use a control group.
I don't know that any data exists.
I did see studies with control groups that suggested that the vaccine did reduce viral load by 30% (when effective to the correct strain), and that could lead to less hospitalizations (because you'll be theoretically less sick), but I don't think there's any clear evidence that it did.