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/src/main.ts

@@ -1,3 +1,5 @@
+import './instrument';
+
 import { ValidationPipe } from '@nestjs/common';
 import { NestFactory } from '@nestjs/core';
 import { DocumentBuilder, SwaggerModule } from '@nestjs/swagger';