Source

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

public function handle_template( $template, $post_id, $validate = false ) {

		if ( $validate && ! array_key_exists( $template, wp_get_theme()->get_page_templates( get_post( $post_id ) ) ) ) {
			$template = '';
		}

		update_post_meta( $post_id, '_wp_page_template', $template );
	}