The API route doesn't render a template. It just outputs the JSON that is passed into render.
You can test this by prepending /api on any route, you'll see JSON output.
The purpose of this is for the AJAX loading of the next page.
A third party library has a CSS file (not a .less file). How can I include it in my plugin. Is plugin.json the right place? If yes, under what subheading shall I place it?
You can use import in one of your less files like this:
@import (inline) './thing.css';
Or you can add an entry to staticDirs
and add it to the header:
https://github.com/NodeBB/nodebb-plugin-emoji/blob/master/lib/index.ts#L80
Or you can add it under the less
array.