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/app/api/sentry-example-api/route.ts

@@ -0,0 +1,17 @@
+import * as Sentry from "@sentry/nextjs";
+export const dynamic = "force-dynamic";
+
+class SentryExampleAPIError extends Error {
+  constructor(message: string | undefined) {
+    super(message);
+    this.name = "SentryExampleAPIError";
+  }
+}
+
+// A faulty API route to test Sentry's error monitoring
+export function GET() {
+  Sentry.logger.info("Sentry example API called");
+  throw new SentryExampleAPIError(
+    "This error is raised on the backend called by the example page.",
+  );
+}