History writes updated Agent.last_message, while sidebar snapshots and saved
chats read AgentContext.last_message. Continuing a chat could therefore leave
its activity timestamp unchanged.
Update the context timestamp in the shared history writer. Preserve explicitly
supplied timestamps across initialization hooks so greeting history does not
make restored chats appear newly active.
Add regression coverage for user, AI, tool, and warning messages in parent and
child contexts, including serialization and continued activity after reload.
Document ownership of the activity timestamp.
Validation: 15 focused tests passed, plus the new regression in the container's
framework runtime. Two live UI messages advanced Thread+ activity timestamps
while preserving creation time; saved JSON and the reloaded UI matched.
