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/instrumentation.ts

@@ -0,0 +1,13 @@
+import * as Sentry from '@sentry/nextjs';
+
+export async function register() {
+  if (process.env['NEXT_RUNTIME'] === 'nodejs') {
+    await import('./sentry.server.config');
+  }
+
+  if (process.env['NEXT_RUNTIME'] === 'edge') {
+    await import('./sentry.edge.config');
+  }
+}
+
+export const onRequestError = Sentry.captureRequestError;