feat(analytics): add PostHog analytics module

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)

Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>

src/shared/posthog.ts

@@ -0,0 +1,46 @@
+import os from "os"
+import { PostHog } from "posthog-node"
+
+type PostHogClient = Pick<PostHog, "capture" | "captureException" | "shutdown">
+
+const NO_OP_POSTHOG: PostHogClient = {
+  capture: () => undefined,
+  captureException: () => undefined,
+  shutdown: async () => undefined,
+}
+
+function shouldDisablePostHog(): boolean {
+  return process.env.OMO_DISABLE_POSTHOG === "true"
+}
+
+function hasPostHogApiKey(): boolean {
+  return (process.env.POSTHOG_API_KEY ?? "").trim().length > 0
+}
+
+function createPostHogClient(options: ConstructorParameters<typeof PostHog>[1]): PostHogClient {
+  if (shouldDisablePostHog() || !hasPostHogApiKey()) {
+    return NO_OP_POSTHOG
+  }
+
+  return new PostHog(process.env.POSTHOG_API_KEY ?? "", options)
+}
+
+export function getPostHogDistinctId(): string {
+  return os.hostname()
+}
+
+export function createCliPostHog(): PostHogClient {
+  return createPostHogClient({
+    host: process.env.POSTHOG_HOST,
+    enableExceptionAutocapture: true,
+    flushAt: 1,
+    flushInterval: 0,
+  })
+}
+
+export function createPluginPostHog(): PostHogClient {
+  return createPostHogClient({
+    host: process.env.POSTHOG_HOST,
+    enableExceptionAutocapture: true,
+  })
+}