As you say, it looks like this isn't possible in the Cloud API. I notice on the Roadmap portal that there are also suggestions and votes for attachment management using the API. You can add your vote to those or suggest your own by following this link
But... the roadmap portal seems to be seldom updated by SmartBear, if at all. I have posted a lot of suggestions in the last 12 months since the portal was released and not a single one has made it onto the board for voting. So while there is a place for ideas and voting, I have zero confidence that it is being used... just setting expectations.
