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/next.config.js

@@ -1,3 +1,5 @@
+const { withSentryConfig } = require('@sentry/nextjs');
+
 /** @type {import('next').NextConfig} */
 const nextConfig = {
   reactStrictMode: true,
@@ -42,4 +44,11 @@ const nextConfig = {
   },
 };
 
-module.exports = nextConfig;
+module.exports = withSentryConfig(nextConfig, {
+  org: process.env.SENTRY_ORG,
+  project: process.env.SENTRY_PROJECT,
+  silent: !process.env.CI,
+  widenClientFileUpload: true,
+  disableLogger: true,
+  automaticVercelMonitors: true,
+});