I ran into this issue today. The problem is that, when using the <script setup> pattern, none of the declared variables are returned. When you get a ref to the component, it's just an empty object. The way to get around this is by using defineExpose in the setup block.

// Child.vue

<template>
  <div ref="wrapper">
   <!-- content ... -->
  </div>
</template>

<script setup>
import { defineExpose, ref } from 'vue'

const wrapper = ref(null)

defineExpose({ wrapper })
</script>

The way you set up the template ref in the parent is fine. The fact that you were seeing empty object { } in the console means that it was working.

Like the other answer already said, the child ref can be accessed from the parent like this: wrapper.value.wrapper.getBoundingClientRect().

The rfc has a section talking about how/why this works: https://github.com/vuejs/rfcs/blob/master/active-rfcs/0040-script-setup.md#exposing-components-public-interface

It's also important to note that, with the <script setup> pattern, your ref in the parent component will not be a ComponentInstance. This means that you can't call $el on it like you might otherwise. It will only contain the values you put in your defineExpose.

Right, so here's what you need to do:

// Parent component
<template>
  <Child :get-ref="(el) => { wrapper = el }" />
</template>

<script setup>
import Child from './Child.vue';
import { ref, onMounted } from 'vue';

const wrapper = ref();

onMounted(() => {
  const rect = wrapper.value.getBoundingClientRect()
  console.log(rect) // works fine!
});
</script>

and

// Child component
<template>
  <div :ref="(el) => { wrapper = el; getRef(el)}">
   // content ...
  </div>
</template>

<script setup>
import { defineProps, ref, onMounted } from 'vue';
  
const props = defineProps({
  getRef: {
    type: Function,
  },
});

const wrapper = ref();

onMounted(() => {
  const rect = wrapper.value.getBoundingClientRect()
  console.log(rect) // works fine!
});
</script>

To learn why, we need to check Vue's documentation on ref: Vue special-attribute 'ref'.

On dynamic binding of (template) ref, it says:

<!-- When bound dynamically, we can define ref as a callback function,
passing the element or component instance explicitly -->
<child-component :ref="(el) => child = el"></child-component>

Since the prop lets you pass data from the parent to a child, we can use the combination of the prop and dynamic ref binding to get the wanted results. First, we pass the dynamic ref callback function into the child as the getRef prop:

<Child :get-ref="(el) => { wrapper = el }" />

Then, the child does the dynamic ref binding on the element, where it assigns the target el to its wrapper ref and calls the getRef prop function in that callback function to let the parent grab the el as well:

<div :ref="(el) => {
            wrapper = el; // child registers wrapper ref
            getRef(el); // parent registers the wrapper ref
            }">

Note that this allows us to have the ref of the wrapper element in both the parent AND the child component. If you wished to have access to the wrapper element only in the parent component, you could skip the child's callback function, and just bind the ref to a prop like this:

// Child component
<template>
  <div :ref="getRef">
   // content ...
  </div>
</template>

<script setup>
import { defineProps } from 'vue';

const props = defineProps({
  getRef: {
    type: Function,
  },
});
</script>

That would let only the parent have the ref to your template's wrapper.

You could get access to the root element using $el field like below:

<template>
  <Child ref="wrapper" />
</template>

<script setup>
import Child from './Child'
import { ref, onMounted } from 'vue'

const wrapper = ref(null)

onMounted(() => {
  const rect = wrapper.value.$el.getBoundingClientRect()
  console.log(rect) 
})
</script

I don't this this is necessarily related to the <script setup> tag. Even in the standard script syntax your second example will not work as-is.

The issue is you are putting ref directly on the Child component:

<template>
  <Child ref="wrapper" />
</template>

and a ref to a component is NOT the same as a ref to the root element of that component. It does not have a getBoundingClientRect() method.

In fact, Vue 3 no longer requires a component to have a single root element. You can define your Child component as :

<template>
  <div ref="wrapper1">// content ...</div>
  <div ref="wrapper2">// content ...</div>
</template>
<script >
import { ref } from "vue";

export default {
  name: "Child",

  setup() {
    const wrapper1 = ref(null);
    const wrapper1 = ref(null);
 
    return { wrapper1, wrapper2 };
  },
};
</script>

What should be the ref in your Parent component now?

Log the wrapper.value to your console from your Parent component. It is actually an object of all the refs in your Child component:

{
  wrapper1: {...}, // the 1st HTMLDivElement
  wrapper2: {...}  // the 2nd HTMLDivElement
}

You can do wrapper.value.wrapper1.getBoundingClientRect(), that will work fine.