quick demo https://1fix.io/blog/2015/12/18/single-request-category-posts/#comment-14862

functions.php

<?php
function my_rest_prepare_term( $data, $item, $request ) {
	$args = array(
		'tax_query' => array(
			array(
				'taxonomy' => $item->taxonomy,
				'field' => 'slug',
				'terms' => $item->slug
			)
		),
		'posts_per_page' => 5
	);
	$posts = get_posts( $args );
	$posts_arr = array();
	foreach ( $posts as $p ) {
		$posts_arr[] = array(
			'ID' => $p->ID,
			'title' => $p->post_title,
			'content' => array(
				'rendered' => apply_filters( 'the_content', $p->post_content )
				)
		);
	}
	$data->data['posts'] = $posts_arr;
	return $data;
}
add_filter( 'rest_prepare_category', 'my_rest_prepare_term', 10, 3 );