[Vuejs]-Update state in parent from slot in Vue

If you read more about slot scope here,

That slot has access to the same instance properties (i.e. the same “scope”) as the rest of the template.

Since, you are passing your form via slot, you would already be having the access to the parent component instance.

Also, as mentioned in the docs, its good to remember

Everything in the parent template is compiled in parent scope; everything in the child template is compiled in the child scope.

So, when you write your component,

<template>
  <ModalComponent>
    <form @submit="toggleModalVisibility"> 
      ...
    </form>
  </ModalComponent>
</template>

any method passed to form will have access to state of the parent component.

Now, if you can just set a data property to toggle the visibity of the modal component in the parent and a method to toggle this property

data: () => {
  return {
    showModal: false //or true
  }
},
methods: {
  toggleModalVisibility() {
    this.showModal = !this.showModal;
  }
}

You can just assign this method to onSubmit handler of the form

form @submit="toggleModalVisibility"