The logic required to populate the right bits of `RoomData` tends towards
the complete `/sync` response struct, so just use the actual response struct
and save the hassle of mapping between the two. It may not make much difference
in its current form, but the next PR will make use of this.

This PR has no functional changes.

This has the following known shortcomings:
 - It doesn't handle missing events not in the from/to range.
 - It doesn't order events in the timeline correctly.
 - It doesn't handle invited/left rooms at all.
 - There is no intelligent wakeup logic: events for Bob will wake up Alice's stream.

Also ensure every sync response has a `next_batch` token by forcing
it in the constructor, as previously timeouts would not have a token.