How can I teach vim about additional C language types for syntax highlighting?

Here is a way to add the names as needed.

For Windows, create (replace vimfiles as appropriate)

~\vimfiles\after\syntax\c.vim

and add lines defining new syntax highlighting items. For example (from my cpp.vim),

" add nullptr as a keyword for highlighting
syn keyword Constant nullptr

To determine which group you want to add to, open a c file and type :syntax and you can look through the existing syntax groups.

I also found out that we can use the match command to cover a set of typedef names described by a pattern:

match Type /\w*_t/

will highlight as a type all typedef names ending in _t (but will do so everywhere, even inside comments and string literals.)