Source

File: wp-includes/rest-api/endpoints/class-wp-rest-posts-controller.php

protected function handle_terms( $post_id, $request ) {
		$taxonomies = wp_list_filter( get_object_taxonomies( $this->post_type, 'objects' ), array( 'show_in_rest' => true ) );

		foreach ( $taxonomies as $taxonomy ) {
			$base = ! empty( $taxonomy->rest_base ) ? $taxonomy->rest_base : $taxonomy->name;

			if ( ! isset( $request[ $base ] ) ) {
				continue;
			}

			$result = wp_set_object_terms( $post_id, $request[ $base ], $taxonomy->name );

			if ( is_wp_error( $result ) ) {
				return $result;
			}
		}
	}