Records session start/end, conversation messages, tool calls, and
errors via better-sqlite3, hooked into RealtimeSession's existing
choke points so no client-side changes are needed. Also fixes a
pre-existing gap where an upstream-initiated disconnect only forwarded
session.closed to the browser without ever calling close(), so no
session end time was ever recorded for that path.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>