File-based conversation store.
 Layout:
   {baseDir}/
     {sessionDir}/
       conversations.json                  — index: every conversation's metadata
       conversations/
         {conversationId}/
           messages.json                   — the full message history (JSON array)
           meta.json                       — conversation-level metadata

 A conversation's id is its (possibly hierarchical) name flattened to a single safe
 folder name, so sub-agent delegations — named "parent/child-turn-n" — each get their
 own folder listed in the index rather than nesting physically. The full name is kept in
 each meta's `ConversationName`.

 {baseDir} is the shared `sessions/` root and paths resolve through `SessionPaths.sessionDir`,
 so a session's conversations nest alongside its tasks, files, observability and feedback
 under one folder, and a task-spawned sub-session's conversations nest beneath that task.