Wordpress_login_signup.php

<form action="<?= admin_url('/admin-ajax.php') ?>" method="POST" enctype="multipart/form-data">
    <input type="hidden" name="action" value="register">
    <input type="email" name="email" value="">
    <input type="password" name="password" value="">
</form>

<?php if(isset($_GET['suceess'])): ?>
<p>succesfil blah blah blah</p>
<?php enif; ?>

<?php

class RegisterForm extends WP_AJAX{
    protected $action = 'register';

    protected function run(){


		$user = wp_insert_user([
			'user_login'   => $this->get('email'),
			'user_email'   => $this->get('email'),
			'user_pass'    => $this->get('password'),
			'display_name' => $this->get('name'),
		]);

		if(is_wp_error($user)){
			$message = 'Register Error';
			$errors = array_keys($user->errors);

			if(in_array('existing_user_login', $errors)){
				$message = 'Email already in use';
			}

			wp_redirect(sprintf("%s/login?message=%s", home_url(), urlencode($message)));
			exit;
		}

		$user = wp_signon([
			'user_login' 	=> $this->get('email'),
			'user_password' => $this->get('password'),
			'remember' 		=> TRUE
		], false);

		wp_redirect(home_url() .'/home?success=true');
		exit;
    }
}