You can use the orderby parameter and pass it an array of what you want to order by in the order you want it ordered by:
https://developer.wordpress.org/reference/classes/wp_query/#order-orderby-parameters
This solves the problem of ordering by post type, and by date, but ordering by term slug or term ID is not something WP_Query can do. It may make sense to you as your posts only appear in a single newsroom_type but nothing prevents an item being both an award and a press release at the same time in the database, so sorting by terms doesn’t make sense, especially since terms have no inherent order that can be used.
The closest is alphabetic, but that complicates sorting further, e.g. if a post has term A and G, does it come after or before a post with the term B? What if B is a child term of G? Sorting by terms is a massive can of worms that has never been tackled or solved. You can’t sort by terms with WP_Query. You can group/search/filter for posts by terms though.
The best way to do this is to instead do 3 separate queries.