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.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;