feat(billing-ui): pricing page, billing settings, and trial banner

Batch 6 - surface the new subscription state in the product:
public pricing page, in-app billing settings tab, and a top-of-
main trial countdown banner.

- frontend/src/app/pricing/page.tsx: public /pricing route, lands
  logged-out users redirected from a 402. Enterprise CTA stubs out
  to mailto:sales@mike.ai (placeholder).
- frontend/src/app/(pages)/account/billing/page.tsx: in-app billing
  settings - current plan, trial status, token usage, manage button
  (Stripe customer portal).
- frontend/src/components/chrome/trial-banner.tsx: countdown banner
  for trialing users, mounted at top of <main> in (pages)/layout.tsx.
- frontend/src/app/(pages)/account/layout.tsx: re-add the "Billing"
  tab (replaces the "Models & API Keys" tab removed in batch 4).
- frontend/src/app/lib/mikeApi.ts: SubscriptionTier/Status/Info
  types + subscription field on UserProfile.
- frontend/src/contexts/UserProfileContext.tsx: thread subscription
  through the profile context.
- backend/src/routes/user.ts: return the subscription block on the
  /user/profile response.
- 5 new tests (3 pricing + 2 billing).

Agent ID: ad65cb0ceb7e70da6 (general-purpose).