Support for Azure DevOps Services and Server are provided over on Stack Overflow currently. Please post your question there.
In terms of work items related to check ins, refer to the Tfvc/Changesets object if you're using TFVC. When creating a changeset you associate the work items with it. It has been a long time since I worked with TFVC but I believe that is what you're looking for. A workspace is simply a local, cached copy of the server project code. TBH TFVC is not really the focus of Azure DevOps/REST APIs so you're going to probably have a harder time doing the same kinds of things over just switching to Git which is where everything is going.