What functionality is missing? What is unsatisfying with the current situation?

The JSON export includes "histories", "Historical Entries", which are created from making events on a timeline, and "Timelines" themselves, but the data does not contain information on which events belong to which timelines. The JSON export would be more complete with this data, so I recommend adding a timelineId field, or some kind of reference field that refers to the right timeline.

How does this feature request address the current situation?

Fixes the problem.

What are other uses for this feature request?

Ensures data ownership and portability for your users. Without this data, events are just a big pile and can't be used anywhere else.