fix(billing): accept BILLING_LIVE=1 in the upgrade nudge (was true-only)

WelcomePage read NEXT_PUBLIC_BILLING_LIVE === "1" but the upgrade nudge read
=== "true", so setting the flag to 1 turned on the welcome copy while leaving
the nudge dark. Both now accept "1" or "true" so the value can't drift.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

Author: gnick18

frontend/src/components/welcome/WelcomePage.tsx

@@ -152,7 +152,9 @@ function R2Demo({ name, label }: { name: string; label: string }) {
  *  Vercel ALONGSIDE the server BILLING_ENABLED / AI_BILLING_ENABLED and redeploy
  *  (see docs/proposals/2026-06-13-billing-go-live-checklist.md). Kept a separate
  *  flag because the server switch is not readable from this client component. */
-const BILLING_LIVE = process.env.NEXT_PUBLIC_BILLING_LIVE === "1";
+const BILLING_LIVE =
+  process.env.NEXT_PUBLIC_BILLING_LIVE === "1" ||
+  process.env.NEXT_PUBLIC_BILLING_LIVE === "true";
 
 
 /** A check glyph for the trust-block lists, sky-blue. The single inline check

frontend/src/lib/billing/upgrade-nudge.ts

@@ -69,7 +69,10 @@ export function subscribeUpgradeNudge(listener: Listener): () => void {
 /** Whether the nudge is active at all (billing live on the client). Dormant in
  *  beta, so callers at produce-feature paywalls can fire freely without guarding. */
 export function isUpgradeNudgeActive(): boolean {
-  return process.env.NEXT_PUBLIC_BILLING_LIVE === "true";
+  // Accept both "1" and "true" so the flag value never has to match exactly one
+  // form, the WelcomePage check reads it the same way.
+  const v = process.env.NEXT_PUBLIC_BILLING_LIVE;
+  return v === "1" || v === "true";
 }
 
 /**