The amount of power Vice Presidents have is entirely dependent on what the President decides to have them do.
Not long ago their job was basically limited to going to funerals and public events the President didn’t have time for.
Harry Truman was only Vice President for 82 days before taking over when Roosevelt died, but as the Wikipedia page says;
"Truman’s brief vice-presidency was relatively uneventful. Roosevelt rarely contacted him, even to inform him of major decisions; the President and Vice President met alone together only twice during their time together in office.
He had rarely discussed world affairs or domestic politics with Roosevelt and was uninformed about major initiatives relating to the war and the top-secret Manhattan Project, which was about to test the world’s first atomic bomb."
About his predecessor;
“Like most Vice Presidents in this era, Garner had little to do, and had little influence on the President’s policies. He famously described the Vice-Presidency as being “not worth a bucket of warm piss”. (For many years, this quote was euphemized as “warm spit”.”