In my personal opinion, breathing techniques are the same as Hamon. The sun breathing technique allows one to turn demons into ash same as Hamon, you might be like 'the other breathing techniques don't do the same thing' to that I say the other techniques originate from the sun breathing technique so they are lesser techniques. Now another thing you might say is 'demons and vampires are not the same' to that I say if you use the stone mask you become a demon or vampire whatever you wanna call it, anyway if you become it you gain the ability to turn other people into your species just weaker than yourself.
I believe that Muzan found a stone mask and used it, some time later Japanese people discovered Hamon but because their culture is WAY different they use it differently. Also the fact that they don't have as much people to develop the techniques compared to everywhere else. Once Japan became connected to the rest of the world they changed the way they used Hamon so breathing techniques became pretty much forgotten.
Now this is probably false cause I don't actually know much just the powers. If you know the story please tell me whether this could possibly happen or if it is just a fantasy that can't happen without changing the story drastically.