feat(observability): integrate Sentry error tracking for API and Web apps

- API: add @sentry/nestjs with instrument.ts, SentryModule, and SentryGlobalFilter
- Web: add @sentry/nextjs with client/server/edge configs, instrumentation hook
- Update next.config.js with withSentryConfig wrapper
- Replace TODO in error.tsx with Sentry.captureException
- Add SENTRY_DSN, SENTRY_AUTH_TOKEN, SENTRY_ORG, SENTRY_PROJECT to .env.example

Co-Authored-By: Paperclip <noreply@paperclip.ing>

apps/web/package.json

@@ -11,6 +11,7 @@
   },
   "dependencies": {
     "@hookform/resolvers": "^5.2.2",
+    "@sentry/nextjs": "^10.47.0",
     "class-variance-authority": "^0.7.1",
     "clsx": "^2.1.1",
     "lucide-react": "^1.7.0",