feat: integrate Sentry for error monitoring in Next.js application

- Added Sentry configuration for edge features in `sentry.edge.config.ts`
- Added Sentry configuration for server-side in `sentry.server.config.ts`
- Created a sample API route to demonstrate error tracking in `src/app/api/sentry-example-api/route.ts`
- Developed a frontend page to trigger and log errors in `src/app/sentry-example-page/page.tsx`
- Configured client-side Sentry initialization in `src/instrumentation-client.ts` with Replay integration
- Implemented instrumentation registration logic in `src/instrumentation.ts`

src/instrumentation-client.ts

@@ -0,0 +1,31 @@
+// This file configures the initialization of Sentry on the client.
+// The added config here will be used whenever a users loads a page in their browser.
+// https://docs.sentry.io/platforms/javascript/guides/nextjs/
+
+import * as Sentry from "@sentry/nextjs";
+
+Sentry.init({
+  dsn: "https://a9390ae6d4b06c851854d48b070bb4cf@o4511511166713856.ingest.us.sentry.io/4511612532228096",
+
+  // Add optional integrations for additional features
+  integrations: [Sentry.replayIntegration()],
+
+  // Define how likely traces are sampled. Adjust this value in production, or use tracesSampler for greater control.
+  tracesSampleRate: 1,
+  // Enable logs to be sent to Sentry
+  enableLogs: true,
+
+  // Define how likely Replay events are sampled.
+  // This sets the sample rate to be 10%. You may want this to be 100% while
+  // in development and sample at a lower rate in production
+  replaysSessionSampleRate: 0.1,
+
+  // Define how likely Replay events are sampled when an error occurs.
+  replaysOnErrorSampleRate: 1.0,
+
+  // Enable sending user PII (Personally Identifiable Information)
+  // https://docs.sentry.io/platforms/javascript/guides/nextjs/configuration/options/#sendDefaultPii
+  sendDefaultPii: true,
+});
+
+export const onRouterTransitionStart = Sentry.captureRouterTransitionStart;