resetting v-model of child component

In my parent component I have something similar to this,

<template>
    <ProductCounter v-model="formData.productCount" label="product count" />
</template>

<script setup>

const initialFormData = {
    productCount: null,
    firstname: '',
    surname: '',
    phone: '',
    email: '',
    postcode: '',
    submittedOnce: false,
    errors: []
}

let formData = reactive({ ...initialFormData });

const clearUI = () => {
    formData = reactive({ ...initialFormData });
    triggerInlineForm.value = false;
}

</script>

My child component looks like this,

<template>
    <div class="form__row" @reset-counts="resetCount">
        <div class="counter__row">
            <label>{{ label }}</label>
            <div class="form__counter">
                <button class="form__button--decrease form__button--circle form__button--animate-scale" :disabled="value == 0 || props.disabled" @click.prevent="decreaseCount()">
                    <i>
                        <FontAwesomeIcon :icon="['fal', 'minus']" />
                    </i>
                </button>
                <input type="text" v-model="value" :disabled="props.disabled" @input="updateQty" placeholder="0"/>
                <button class="form__button--increase form__button--circle form__button--animate-scale" :disabled="props.disabled" @click.prevent="increaseCount()">
                    <i>
                        <FontAwesomeIcon :icon="['fal', 'plus']" />
                    </i>
                </button>
            </div>
        </div>
    </div>
</template>

<script setup>
import { FontAwesomeIcon } from '@fortawesome/vue-fontawesome';

const emits = defineEmits(['update:modelValue', 'resetCounts']);

const props = defineProps({
    label: {
        type: String,
        required: true
    },
    modelValue: {
        type: String,
        required: true,
        default: 0
    },
    disabled: {
        type: Boolean,
        required: false
    }
});

const value = ref(props.modelValue);

const updateQty = () => {
    emits('update:modelValue', value.value)
}

const increaseCount = () => {
    value.value++
    emits('update:modelValue', value.value)
}

const decreaseCount = () => {
    value.value--;
    emits('update:modelValue', value.value)
}

</script>

I would expect that when clearUI is fired from the parent, and formData gets reset the v-model of ProductCounter should reflect that go back to 0 but it does not, where am I going wrong?

The link to live solution

Please prepare minimum reproducible example the next time on https://play.vuejs.org/. And to your question:

You SHOULD NOT overwrite reactive variables in Vue please...

Just mutate them Object.assign(formData, initialFormData):

Also don't dereference component properties: const value = ref(props.modelValue). The properties lose their reactivity because you just a copy a primitive value.

The best way to create a v-model pattern is to use computed which you can manipulate directly in the template.

const value = computed({
  get(){
    return props.modelValue;
  },
  set(val){
    emits('update:modelValue', val);
  }
});

Also your count property should be a number, not a string (you get Vue warnings):

    modelValue: {
        type: Number,
        required: true,
        default: 0
    },

Also there's no need to update the prop on the input event, since you're already using v-model on the <input>. Also you should convert your input's model to a number:

 <input type="text" v-model.number="value" :disabled="props.disabled" placeholder="0"/>

So you have:
App.vue

<template>
  	<p>
  	  <ProductCounter v-model="formData.productCount" label="product count" />
    </p>
    <button @click="clearUI">
      Clear
  	</button>
    <div>
      {{ JSON.stringify(formData) }}
  </div>
</template>

<script setup>
import ProductCounter from './ProductCounter.vue'
import {reactive} from 'vue'
  
const initialFormData = {
    productCount: 0,
    firstname: '',
    surname: '',
    phone: '',
    email: '',
    postcode: '',
    submittedOnce: false,
    errors: []
}

let formData = reactive({ ...initialFormData });

const clearUI = () => {
    Object.assign(formData, initialFormData);
}

</script>

ProductCounter.vue:

<template>
    <div class="form__row">
        <div class="counter__row">
            <label>{{ label }}</label>
            <div class="form__counter">
                <button :disabled="value == 0 || props.disabled" @click.prevent="value--">
                -
                </button>
                <input type="text" v-model.number="value" :disabled="props.disabled" placeholder="0"/>
                <button :disabled="props.disabled" @click.prevent="value++">
                 +
                </button>
            </div>
        </div>
    </div>
</template>

<script setup>
import {computed} from 'vue';
const emits = defineEmits(['update:modelValue']);

const props = defineProps({
    label: {
        type: String,
        required: true
    },
    modelValue: {
        type: Number,
        required: true,
        default: 0
    },
    disabled: {
        type: Boolean,
        required: false
    }
});

const value = computed({
  get(){
    return props.modelValue;
  },
  set(val){
    emits('update:modelValue', val);
  }
});


</script>

When you override formData in clearUI(), you change the content of the variable:

let formData = reactive({ ...initialFormData });

const clearUI = () => {
    formData = reactive({ ...initialFormData });
}

However, this does not change the object that was bound to the template during component setup. You can fix this using ref and assigning to its value:

const formData = ref({ ...initialFormData });

const clearUI = () => {
    formData.value = { ...initialFormData };
}

or you can override the properties individually:

const formData = reactive({ ...initialFormData });

const clearUI = () => {
    Object.assign(formData, initialFormData);
}

A second problem is that you are setting the value in ProductCounter to the initial value of props.modelValue, but that is the literal value, not a reactive property. So when props.modelValue changes, value does not. To fix it, you can add a watcher:

const value = ref(props.modelValue);
watch(
  () => props.modelValue,
  () => value.value = props.modelValue
)

Now value will be adjusted when props.modelValue changes.

Here it is in a playground