The number of buttons on the front closure or on the sleeve has nothing to do with rules but is simply a matter of style.

There are, and have, been styles of jackets with one, two, three, and many more buttons on the front.

The number of buttons on the cuff is a little bit more regimented but still a matter of style.
Many Bespoke Tailors maintain that the only "proper" number of buttons on the cuff is four. They also maintain that the buttons should be in actual button holes and really work. My Bespoke suits have this feature but I have never seen an off-the-rack suit with it.

I chose three buttons on my Jackets more as a symbol that they are Made-to-Measure versus Custom or Bespoke. Plus, I like that style.

By the way, a three button front closure Jacket is only buttoned with the middle button. A two button Jacket is buttoned with both. A one Button Jacket is usually designed not to be buttoned at all.