Source

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

protected function check_delete_permission( $post ) {
		$post_type = get_post_type_object( $post->post_type );

		if ( ! $this->check_is_post_type_allowed( $post_type ) ) {
			return false;
		}

		return current_user_can( 'delete_post', $post->ID );
	}