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/api/package.json

@@ -27,6 +27,8 @@
     "@paralleldrive/cuid2": "^3.3.0",
     "@prisma/adapter-pg": "^7.7.0",
     "@prisma/client": "^7.7.0",
+    "@sentry/nestjs": "^10.47.0",
+    "@sentry/profiling-node": "^10.47.0",
     "@willsoto/nestjs-prometheus": "^6.1.0",
     "bcrypt": "^6.0.0",
     "class-transformer": "^0.5.1",