Currently it's possible to cancel a reindexing task only during step 3 "reindexing documents from the old index into the new index". I think that is not a straightforward UI from the user's perspective. I think we should make it possible to cancel the reindexing task from the start up until a moment when the old index is being deleted (step 4).
There is logic in place that allows us to clean up the cancelled task and start it over. We would need to update this check on the server side.