Javascript Place Image Where User Clicks

I think best would be just to set left and top using % units. You can do the same for the width of the marker.

const rect = document.getElementById('map1').getBoundingClientRect();
const originalWidth = rect.width
const originalHeight = rect.height


window.addEventListener("load", function() {
  document.getElementById('map1').onclick = function(event) {
    const rect = event.target.getBoundingClientRect();
    const x = event.clientX - rect.left;
    const y = event.clientY - rect.top;
    addMarker(x, y, rect.width, rect.height);
  }
});


function resize() {
  document.getElementById('map1').style.width = ((Math.random() * 50) + 50) + "%"
}

function addMarker(x, y, w, h) {
  var i = new Image();
  i.src = 'https://placehold.co/32x32/000000/FFF';
  i.style.position = "absolute";
  i.onload = function() {
    var xOffset = x;
    var yOffset = y;

    // center image on cursor

    xOffset -= i.width / 2;
    yOffset -= i.height / 2;

    // Set image insertion coordinates
    i.style.left = (xOffset / w * 100) + '%';
    i.style.top = (yOffset / h * 100) + '%';

    // optionally: 
    i.style.width = (i.width / originalWidth * 100) + '%'

  }

  // Append the image to the DOM
  document.getElementById('map1').appendChild(i);

}

.responsive {
  position: relative;
  max-width: 1200px;
  width: 100%;
  height: auto;
  border: 1px solid red;
}

.responsive #myImg {
  width: 100%;
  display: block;
}

<div class="container">
  <div style="height: auto; padding: 3px 0 3px 0;">
    <div class="card">
      <div class="card_content">
        <p>click to place markers <button onclick="resize()">random size</button></p>
        <div id="map1" class="responsive">
          <img src="https://picsum.photos/800/300" id="myImg">
        </div>
      </div>
    </div>
  </div>
</div>

To achieve what you're looking for, you need to listen for a few different events.

I'll give you this code snippet I wrote based on your codepen. It detects the events you'll need to look for.

1. Window Resize
2. Image Scaling up/down
3. Extra check: checking if the image itself was resized (if you add the ability later in your code)

document.addEventListener('DOMContentLoaded', function() {
    // Get the reference to the div container
    const mapContainer = document.getElementById('map1');

    // Find the image inside the container
    const imageElement = mapContainer.querySelector('img');

    // Add event listener to window resize event
    window.addEventListener('resize', function() {
        console.log('Window resized');
        // Detect if the image was scaled
        detectImageScaling();
    });

    // Add event listener to image resize event
    const imageResizeObserver = new ResizeObserver(entries => {
        for (let entry of entries) {
            console.log('Image resized');
        }
    });

    // Start observing the image element
    imageResizeObserver.observe(imageElement);

    // Function to detect scaling changes of your map1.img
    function detectImageScaling() {
        const currentWidth = imageElement.clientWidth;
        const currentHeight = imageElement.clientHeight;

        // Check if the width or height has changed since the last check
        if (imageElement.dataset.prevWidth !== currentWidth || imageElement.dataset.prevHeight !== currentHeight) {
            if (imageElement.dataset.prevWidth && imageElement.dataset.prevHeight) {
                const scalingFactorX = currentWidth / imageElement.dataset.prevWidth;
                const scalingFactorY = currentHeight / imageElement.dataset.prevHeight;

                if (scalingFactorX > 1 || scalingFactorY > 1) {
                    console.log('Image scaled up');
                } else if (scalingFactorX < 1 || scalingFactorY < 1) {
                    console.log('Image scaled down');
                }
            }

            // Update previous width and height
            imageElement.dataset.prevWidth = currentWidth;
            imageElement.dataset.prevHeight = currentHeight;
        }

        // Call this function recursively to continue detecting scaling changes
        requestAnimationFrame(detectImageScaling);
    }
});