The shared shell cache codec never overrode activityRunStartedAt and
unsettledAt with DateTimeUtcFromString, so any snapshot holding a working or
unsettled thread encoded fine but failed to decode on the next cold launch.
The store discarded the whole row and the Home list stayed empty until the
environment reconnected.

Add the two overrides and extend the mobile cache round-trip test with a
running, unsettled thread so the codec and the JSON overrides stay in sync.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>