Capture-health line in hyp status #810

Parent

Implementation spec: #798 (LLP 0245). Discharges RFC 0245 open question 1's duty.

What to build

Silent capture gaps become visible: the listener source's status details carry the last event seen, and hyp status renders a capture-health line comparing it to the last transcript activity. When the gap exceeds a threshold, a diagnostics entry appears with a repair hint and a severity that can degrade the overall status. Status keeps answering from the status file only (no dataset or cache reads).

Acceptance criteria

• hyp status (text and json) shows the capture-health line when claude is OTEL-attached
• Diagnostics entry fires past the threshold and can degrade overall status
• Line absent when not attached (no noise)
• Covered by a status-diagnostics-style smoke plus unit tests for the render and threshold

Blocked by

• Tracer bullet: claude OTLP listener captures a session into ai_gateway_messages #803