fix(website): fall back to US PostHog host when env is empty string

GitHub Actions expands an unset `POSTHOG_HOST` secret to "", which
passes the nullish check (`??`) and leaves api_host empty. PostHog
then falls back to the current origin and sends POST /e/ to
cubepi.pages.dev — Cloudflare Pages doesn't accept POST and returns
405, so no events reach PostHog.

Switch both the build-time embed and the client init to `||` so an
empty string also routes to https://us.i.posthog.com.

Author: xfgong

website/docusaurus.config.ts

@@ -2,8 +2,12 @@ import type { Config } from '@docusaurus/types';
 import type { Options as ClassicOptions } from '@docusaurus/preset-classic';
 import { themes as prismThemes } from 'prism-react-renderer';
 
-const POSTHOG_KEY = process.env.POSTHOG_KEY ?? '';
-const POSTHOG_HOST = process.env.POSTHOG_HOST ?? 'https://us.i.posthog.com';
+// Use `||` not `??` here: GitHub Actions expands an unset secret to "" (an
+// empty string passes the nullish check, so `??` would leave api_host empty
+// and PostHog falls back to the current origin — sending POST /e/ to the
+// docs domain and hitting a 405 from Cloudflare Pages).
+const POSTHOG_KEY = process.env.POSTHOG_KEY || '';
+const POSTHOG_HOST = process.env.POSTHOG_HOST || 'https://us.i.posthog.com';
 const GIT_SHA = process.env.GITHUB_SHA?.slice(0, 7) ?? 'dev';
 
 const classicOptions: ClassicOptions = {

website/src/clientModules/posthog.ts

@@ -1,8 +1,10 @@
 import posthog from 'posthog-js';
 import siteConfig from '@generated/docusaurus.config';
 
-const key   = (siteConfig.customFields?.POSTHOG_KEY  as string | undefined) ?? '';
-const host  = (siteConfig.customFields?.POSTHOG_HOST as string | undefined) ?? 'https://us.i.posthog.com';
+// Use `||` not `??`: the build embeds POSTHOG_HOST="" when the secret is
+// unset, and we need the empty string to fall back to the US endpoint.
+const key  = (siteConfig.customFields?.POSTHOG_KEY  as string | undefined) || '';
+const host = (siteConfig.customFields?.POSTHOG_HOST as string | undefined) || 'https://us.i.posthog.com';
 
 if (typeof window !== 'undefined' && key) {
   posthog.init(key, {