Smaller header logo on mobile only

inside this container you selected there is the anchor (a-tag) and inside this the logo file itself ( depends on your logo format: img or an inline svg)
so try the selector: #header .logo img or if you are using svg files : #header .logo svg

next you do not need to use the switch point to hamburger for that rule.
you can use the media query – when you need it f.e.:

@media only screen and (max-width:479px) {
  #header .logo img {
    transform: scale(0.8);
    transform-origin: center left;
  }
}