REST API retrieving posts from www.sitename.com/category/news/ instead of just just from www.sitename.com

If you want to retrieve posts, you need to use the posts endpoint for starters, not pages. So that’s wp-json/wp/v2/posts. The documentation for that endpoint is here.

As you can see in the documentation, under List Posts, you can retrieve posts for a specific category using the categories argument. However, you need to use the category ID, not the slug.

http://example.com/wp-json/wp/v2/posts/?categories=14

If you absolutely must use the slug, then you need to retrieve that first, from the categories endpoint:

http://example.com/wp-json/wp/v2/categories/?slug=news

That will retrieve any categories with news as the slug. This response will include the category ID which you can store and use to query posts with that category.