feat: add trace-level input/output to Langfuse observability (#69)

* feat: add trace-level input/output to Langfuse observability

- Add @langfuse/client and @langfuse/tracing dependencies
- Wrap POST handler with observe() for proper tracing
- Use updateActiveTrace() to set trace input, output, sessionId, userId
- Filter Next.js HTTP spans in shouldExportSpan so AI SDK spans become root traces
- Enable recordInputs/recordOutputs in experimental_telemetry

* refactor: extract Langfuse logic to separate lib/langfuse.ts module

package.json

@@ -17,7 +17,9 @@
         "@ai-sdk/google": "^2.0.0",
         "@ai-sdk/openai": "^2.0.19",
         "@ai-sdk/react": "^2.0.22",
+        "@langfuse/client": "^4.4.9",
         "@langfuse/otel": "^4.4.4",
+        "@langfuse/tracing": "^4.4.9",
         "@next/third-parties": "^16.0.6",
         "@openrouter/ai-sdk-provider": "^1.2.3",
         "@opentelemetry/sdk-trace-node": "^2.2.0",