This has currently been implemented in the timeline model, the trip
grouping and the live data handling, duplicating this rather complex
logic multiple times. The goal is to replace all that with the new code.

Compared to the existing implementations, this has more fine-grained
change notifications for the various corner cases, and it persists the
batching, so we don't have to compute that on every startup again.

This also makes further optimizations possible, like persisting the sort
order of the batches, so we only need to load the reservation elements
actually on the screen.