Geting values for multipart form elements using Twig
I think you are just overlooking something simple here. The 'multi part form elements' is called a composite element. And it holds an array of values of its subfields. 

Let's say the composite parent is called 'name', and it has a subfield called first_name, then you can use {{ data.name.first_name }} to get the first name in twig. 

As for webform submission token, you can try something like [webform_submissions:values:name:first_name]