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

lib/langfuse.ts

@@ -0,0 +1,63 @@
+import { observe, updateActiveTrace } from '@langfuse/tracing';
+import * as api from '@opentelemetry/api';
+
+// Check if Langfuse is configured
+export function isLangfuseEnabled(): boolean {
+  return !!process.env.LANGFUSE_PUBLIC_KEY;
+}
+
+// Update trace with input data at the start of request
+export function setTraceInput(params: {
+  input: string;
+  sessionId?: string;
+  userId?: string;
+}) {
+  if (!isLangfuseEnabled()) return;
+
+  updateActiveTrace({
+    name: 'chat',
+    input: params.input,
+    sessionId: params.sessionId,
+    userId: params.userId,
+  });
+}
+
+// Update trace with output and end the span
+export function setTraceOutput(output: string) {
+  if (!isLangfuseEnabled()) return;
+
+  updateActiveTrace({ output });
+  const activeSpan = api.trace.getActiveSpan();
+  if (activeSpan) {
+    activeSpan.end();
+  }
+}
+
+// Get telemetry config for streamText
+export function getTelemetryConfig(params: {
+  sessionId?: string;
+  userId?: string;
+}) {
+  if (!isLangfuseEnabled()) return undefined;
+
+  return {
+    isEnabled: true,
+    recordInputs: true,
+    recordOutputs: true,
+    metadata: {
+      sessionId: params.sessionId,
+      userId: params.userId,
+    },
+  };
+}
+
+// Wrap a handler with Langfuse observe
+export function wrapWithObserve<T>(
+  handler: (req: Request) => Promise<T>
+): (req: Request) => Promise<T> {
+  if (!isLangfuseEnabled()) {
+    return handler;
+  }
+
+  return observe(handler, { name: 'chat', endOnExit: false });
+}