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/app/error.tsx

@@ -1,5 +1,6 @@
 'use client';
 
+import * as Sentry from '@sentry/nextjs';
 import { useEffect } from 'react';
 
 export default function GlobalError({
@@ -10,11 +11,8 @@ export default function GlobalError({
   reset: () => void;
 }) {
   useEffect(() => {
-    // Report to error tracking service in production; log digest only
-    if (process.env.NODE_ENV === 'production') {
-      // TODO: integrate with Sentry/Datadog when available
-      // errorReporter.captureException(error);
-    } else {
+    Sentry.captureException(error);
+    if (process.env.NODE_ENV !== 'production') {
       console.error('Unhandled error:', error);
     }
   }, [error]);