Use the mousedown event type instead of click

yourThing.addEventListener(`mousedown`, clickThing)

Check the MouseEvent buttons property

function clickThing(event) {
  if (event.buttons == 1) { // check if the left mouse button is pressed
    // your left click code here
  }
  else if (event.buttons == 2) { // check if the right mouse button is pressed
    // your right click code here
  }
}

Disable the context menu with the contextmenu event type

yourThing.addEventListener(`contextmenu`, disableContextMenu)

function disableContextMenu(event) {
  // the default browser action is to show the context menu
  // this prevents the default browser action from happening
  event.preventDefault()
}