feat(usage): replay last-known plan usage in the SSE init snapshot

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>

src/web/routes/status-telemetry-routes.ts

@@ -23,6 +23,7 @@ import {
   type RawStatuslinePayload,
 } from '../../usage-telemetry.js';
 import { SessionStatusTelemetry } from '../sse-events.js';
+import { setLatestPlanUsage } from '../plan-usage-latest.js';
 import type { SessionPort, EventPort } from '../ports/index.js';
 
 export function registerStatusTelemetryRoutes(app: FastifyInstance, ctx: SessionPort & EventPort): void {
@@ -56,7 +57,9 @@ export function registerStatusTelemetryRoutes(app: FastifyInstance, ctx: Session
             if (!ctx.sessions.has(id)) lastSig.delete(id);
           }
         }
-        ctx.broadcast(SessionStatusTelemetry, { sessionId, ...telemetry });
+        const payload = { sessionId, ...telemetry };
+        setLatestPlanUsage(payload); // replayed in the SSE init snapshot for fresh loads
+        ctx.broadcast(SessionStatusTelemetry, payload);
       }
     }