First you can use more specific the_content_feed hook, so your code doesn’t have to run in unrelated contexts.
The “type” refers to feeds (not posts), so it would be something like rss2 and it will be same across post types.
It is a little unobvious, but feeds are also kind of a Loop, same as on front end. So same APIs typically work just fine.
Your check can be something like if ( 'books' === get_post_type() ).