This feature is available in all editions.
On the Sprint/Iteration Tracking page for one particular sub-project, the progress bar shows that no work has been done even though there are hours shown in the Done column of the tasks page. A team member added some completed effort. His completed effort (4 hrs) displays in the Done column and in the progress bar. The other hours in the Done column still don't show up in the progress bar. Why is there a difference?
The progress bar for a sprint/iteration includes all effort that was tracked within the current iteration. It sounds like there are items in this sprint that had effort tracked against them in a previous sprint that were moved forward into the current sprint. Effort tracked in previous sprint will not show in the current sprint. But, when you look at the individual task, the accumulated Effort on the task across all sprint is shown.
You can use the Effort Quicklist report to see Effort transactions that were logged for the tasks that have been split across multiple iterations. Here, you can see the specific task, sprint, and project to which the hours were assigned.
Splitting workitems when closing a sprint separates completed work from incomplete work. Splitting an incomplete item creates two separate backlog items and pushes the new backlog item forward with all associated estimates. You can adjust the estimates on the new item if you need to.