Did you add the property to your Vue component as well? It might also have to do with how you call the token. I believe you need {!! csrf_token() !!} instead.
It's also highly recommended to do this kind of stuff on a global base. So instead of passing it to a component so pass the variable of the csrf token to a global variable which you can use in all your other components
You have multiple options here, but it's recommended to do it in the head of your html
// app.blade.php
<!doctype html>
<html>
<head>
<meta name="_token" content="{!! csrf_token() !!}"/>
</head>
<body>
// Include your vuejs script here
</body>
</html>
When you do an ajax request for example you can fetch the token from the head of the document. Here is an example with jQuery, but you can do it with any kind of JS
// app.js
$.ajax({
url: http://someurl.com/update,
type: 'POST',
headers: {
'X-CSRF-Token': $('meta[name=_token]').attr('content')
},
data: {
'username': 'new_username'
}
}).done(function () {
alert('done');
});