The header chip previously only repopulated on reload from per-browser
localStorage, so a fresh browser (or cleared storage) stayed blank until a
session next rendered telemetry. Store the latest broadcast telemetry
process-wide (plan-usage-latest.ts) and include it as `planUsage` in
getLightState — the per-connection SSE init snapshot — so handleInit paints
the chip immediately on every fresh load / reconnect, authoritative over the
localStorage restore. Null until the first telemetry of the process.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
