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/public/app.js

@@ -2258,6 +2258,10 @@ class CodemanApp {
     this._serverCjkOverride = data.inputCjkForm || false;
     this._updateCjkInputState();
 
+    // Plan-usage chip: server's last-known telemetry, so it shows immediately on
+    // a fresh load / reconnect (authoritative; wins over the localStorage restore).
+    if (data.planUsage) this.updatePlanUsageChip(data.planUsage);
+
     // Update version displays (header and toolbar)
     if (data.version) {
       const versionEl = this.$('versionDisplay');