Auto mode availability is now tracked as ongoing telemetry

What

• A new diagnostic snapshot function builds a combined object describing Claude's "auto mode" state: whether it's available, why it isn't if not, whether it's disabled by settings or policy (and which), whether it's disabled by trusted policy, its enabled state and source, whether its circuit breaker has tripped, the default permission mode, and whether it fell back.
• Startup (init) telemetry can now include this snapshot (fields like autoModeAvailable, autoModeCircuitBroken, etc.), gated by a new logAutoModeAvailability flag, and a change tracker is registered so a tengu_auto_mode_availability_changed event fires later if auto mode's availability flips during the session.
• The context-metrics call at startup is now wrapped so a failure is caught and logged ("context metrics failed") instead of throwing synchronously.

Why This gives visibility into whether and why auto mode is available, both at startup and if its availability changes mid-session, and makes startup telemetry collection more resilient to unrelated failures.