What do astronomers do different now that they know about fusion of the Sun? I would like to know how knowledge of the fusion in the Sun has changed how astronomers explore the universe. What do astronomers do differently now that we know that the Sun’s use of proton-to-proton chain to create energy? Please include sources.
How has knowledge of fusion of the Sun changed astronomy?

TL;DR: It changed everything.
Up until the 1930s, physicists and astronomers argued for a rather young universe while geologists and biologists argued for a markedly older Earth. The problem was that physicists and astronomers couldn't image any known processes that would possibly allow the Earth to be as old as geologists and biologists claimed. Note well: geologists and biologists of that time were not arguing for an Earth that is 4.55 billion years old. They were wanting an Earth that was at least several hundred million years old.
Hans Bethe's 1938 paper, along with a few papers that immediately preceded Bethe's paper, paved the way for addressing that discrepancy. It wasn't until the 1950s when Clair Cameron Patterson showed that the Earth was much older than geologists and biologists thought. The 1950s also were when the apparently ridiculous claims of an expanding universe finally become accepted.