It still is a republic because that’s the way the Constitution set it up and that has not changed yet.
People act like it’s a democracy and in many ways it does function that way, much to the detriment of us all.
This short little 10 min video explains it very well.
Types of Government, Explained
https://www.youtube.com/watch?v=N4r0VUybeXY
The disaster at Appomattox severely crippled the United States constitution.
The original constitution provided for limited, enumerated powers for the federal government.
Today we have a synthetic constitution, plus a two million page Federal Register so Washington can control every aspect of our lives. Even the size of mud flaps on trucks using state-funded highways.