We use the folio to show some description and more information about a task for the users because the ootb worklist only shows process data which is not sufficient for the business. AFAIK the folio is the only flexible field, but I can only set it from within the same process and not by a SMO method from another (background) process which is checking related information about an approval in another LOB system.

You could do this with a custom broker, but our policy is not to use custom brokers anymore to become cloud ready. So the request is either providing this as an ootb SMO method or - and this is maybe even more scalable - providing a K2 API in the K2 cloud to get access to these things from our solutions.