In almost all cases, people say "do you have any updates?". Whether it's for work or for a software, updates is plural because it's generalized.
I think with the technology age that we live in, we are used to hearing updates. An example of this is: do you have any updates to the program. I feel that the second option is more correct in plain English, as in do you have any update to the situation. It sounds more right to me. Thank you.