docs: refresh stale docs to match current implementation

Documentation pass — reviewed codebase in full, identified stale references,
and aligned docs with actual code state.

Changes:
- CLAUDE.md, PRODUCTION_SETUP.md, LAUNCH_CHECKLIST.md, src/auth.config.ts:
  middleware path src/middleware.ts → src/proxy.ts (Next.js 16+ convention)
- CLAUDE.md, ENVIRONMENT.md, README.md:
  dev server port localhost:3000 → localhost:4000 (per package.json dev
  script 'next dev --webpack -H 0.0.0.0 -p 4000')
- PRODUCTION_DEPLOYMENT_CHECKLIST.md:
  rewrote migration list — actual db/migrations/ contains 10 files
  (0000–0091), not the Supabase-era 001–092 series. Updated platform
  version 1.6 → 2.0 and last-updated stamp.
- MEMORY.md:
  refreshed 'Last updated' to 2026-06-25 and added a current-state header
  flagging the 'Auth.js v5 wiring' section as historical (current auth
  is Neon Auth/Better Auth). Also flags the 'GitHub origin' notes as
  historical (only Gitea origin exists).
- LAUNCH_CHECKLIST.md:
  added 'Last updated: 2026-06-25' header and refresh note in footer.

Verification:
- npx tsc --noEmit: pre-existing Stripe API version + test mock errors
  only (verified by stashing changes and re-running — same error set).
- No new errors introduced.

PRODUCTION_SETUP.md

@@ -24,7 +24,7 @@ npm run dev
    NEON_AUTH_COOKIE_SECRET=<openssl rand -base64 32>
    NEXT_PUBLIC_SITE_URL=https://yourdomain.com
    ```
-3. Configure middleware in `src/middleware.ts`
+3. Configure middleware in `src/proxy.ts`
 
 ### 2. Stripe Payments
 
@@ -74,7 +74,7 @@ Ensure environment variables are set before deployment.
 
 ## Key Files
 
-- `src/middleware.ts` - Neon Auth (Better Auth) middleware
+- `src/proxy.ts` - Neon Auth (Better Auth) middleware
 - `src/lib/stripe-billing.ts` - Stripe integration
 - `src/lib/analytics.ts` - PostHog analytics
 - `src/lib/sentry.ts` - Sentry error tracking