feat: integrate Sentry error monitoring for client and backend

[Vivian-04]

PR #168 Add Sentry error monitoring for both client and backend

Description

This PR implements comprehensive error tracking and monitoring across the entire SYNCRO stack by integrating Sentry.

Key Changes

Backend (/backend)

• Sentry SDK Integration: Installed @sentry/node and @sentry/profiling-node.
• Initialization: Configured Sentry at the top of src/index.ts with profiling and tracing enabled.
• Middleware: Integrated Sentry.Handlers.requestHandler() at the beginning of the middleware stack and Sentry.Handlers.errorHandler() at the end.
• User Context: Updated the authenticate and optionalAuthenticate middlewares to automatically enrich Sentry events with user IDs and emails.
• Environment: Updated .env.example with the required Sentry configuration variables.

Client (/client)

• Sentry Next.js SDK: Installed @sentry/nextjs.
• Unified Config: Created sentry.client.config.ts, sentry.server.config.ts, and sentry.edge.config.ts.
• Build Integration: Wrapped next.config.mjs with withSentryConfig to enable automatic source map uploads and build-time instrumentation.
• Environment: Added NEXT_PUBLIC_SENTRY_DSN and deployment variables to .env.example.

Stability and Fixes

During verification, several pre-existing issues were identified and resolved to ensure a clean build and reliable monitoring:

• Backend: Fixed a syntax error in risk-detection-service.ts.
• Client:
  • Fixed duplicate imports and syntax garbage in subscriptions.tsx.
  • Resolved a TypeScript type mismatch in cancellation-guide-modal.tsx.
  • Fixed a visibility access error and duplication in audit-log.ts.

Verification

• Verified backend initialization and middleware placement.
• Verified client configuration and build-time wrapping.
• Successfully completed production builds (npm run build) in both directories following the fixes.

Next Steps

1. Add SENTRY_DSN, SENTRY_ORG, and SENTRY_PROJECT to the production .env files.
2. Generate a SENTRY_AUTH_TOKEN for source map uploads during CI/CD.

Closes #168

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[Vivian-04]

Kindly confirm.