I haven’t look for studies specifically, if you could link some that would be great.

I just hear anecdotal evidence like “hospitalizations have gone down”. Which may be 100% true, but is hardly evidence that the vaccines are effective. The placebo effect is well known. It’s not shocking that hospitalization has gone down when the media has been beating the fear drum on how terribly dangerous the virus is 24/7, causing people to panic (pre vaccine days) and go to the hospital out of caution. Along comes a vaccine that is touted as effective and the media pounds that drum 24/7 and hospitalization goes down. The vaccine could have been saline solution and you would have seen a drop in hospitalization.