It looks like I am able to get the same behavior you're showing in your example by console logging both of the ids. However, it seems like the recurrenceId isn't being set until the editor is opened, and is still equal to 0 in the template (I've attached a screenshot illustrating this). This means that I can't use the recurrenceId as an id for my button in my template.
To give you some more background, we're using the scheduler to store short news stories that will be displayed on a scheduled date. The button I have in my template allows users to preview what the story will look like. Since this depends on an id, the preview is currently working for non-recurring events, as well as the first occurrence for recurring events. It, however, is not working for subsequent occurrences because the id is 0.
Can you think of any other ways I might be able to identify which story goes with subsequent occurrences of an recurring event?
Thank you for your help!