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/plan-usage-latest.ts

@@ -0,0 +1,22 @@
+/**
+ * @fileoverview Process-wide last-known plan-usage telemetry (account-global).
+ *
+ * The status-telemetry route writes the latest broadcast value here; the SSE
+ * init snapshot (`getLightState`) replays it so the header "Plan Usage Limits"
+ * chip shows immediately on a fresh page load / SSE reconnect — before any new
+ * statusline render arrives, and without relying on per-browser localStorage.
+ *
+ * Null until the first telemetry of the process; cleared naturally on restart.
+ *
+ * @module plan-usage-latest
+ */
+
+let latest: Record<string, unknown> | null = null;
+
+export function setLatestPlanUsage(value: Record<string, unknown>): void {
+  latest = value;
+}
+
+export function getLatestPlanUsage(): Record<string, unknown> | null {
+  return latest;
+}