Custom Form Validation with Vue.js

# Introduction

In this challenge, you will learn how to create a custom form validator in a web application. You will be provided with the initial code structure, including Vue.js components and utility functions. Your task is to complete the missing parts in the code to implement the custom form validation functionality, including updating the input value, validating the email format, and implementing the form validation logic. By completing this challenge, you will gain practical experience in building custom form validation mechanisms, which is a common requirement in web development.