How to add one event listener for all buttons

If the buttons do not have a common class, you can use:

button[id^=but]

To select any button with id starting with the phrase but, so it translates to but*, where * is a wildcard match.

const btns = document.querySelectorAll('button[id^=but]')

btns.forEach(btn => {

   btn.addEventListener('click', event => {
        console.log( event.target.id );
   });

});

<button id='but1'>Button1</button>
<button id='but2'>Button2</button>
<button id='but3'>Button3</button>
<button id='but4'>Button4</button>

In this case, you could use a class instead of id to grab every button.

<button class="btn">
Button1
</button>
<button class="btn">
Button2
</button>
<button class="btn">
Button3
</button>
<button class="btn">
Button4
</button>

And then in JS:

const buttons = document.querySelectorAll('.btn')
buttons.forEach(function(currentBtn){
  currentBtn.addEventListener('click', handleEvent)
})

You just loop over the buttons constant which hold a NodeList with all the buttons that were found. read about document.querySelectorAll

You don't really need to add listeners to all the buttons. There is such thing in JS as Bubbling and capturing so you can wrap all your buttons with a div and catch all the events there. But make sure you check that the click was on a button and not on the div.

const wrapper = document.getElementById('wrapper');

wrapper.addEventListener('click', (event) => {
  const isButton = event.target.nodeName === 'BUTTON';
  if (!isButton) {
    return;
  }

  console.dir(event.target.id);
})

div {
  padding: 20px;
  border: 1px solid black;
}

<div id='wrapper'>
  <button id='but1'>
  Button1
  </button>
  <button id='but2'>
  Button2
  </button>
  <button id='but3'>
  Button3
  </button>
  <button id='but4'>
  Button4
  </button>
</div>