docs: refactor analytics + remove segment (#13954)

* docs: refactor analytics + remove segment

* small refactor of condition

www/apps/ui/providers/index.tsx

@@ -25,10 +25,7 @@ type ProvidersProps = {
 
 const Providers = ({ children }: ProvidersProps) => {
   return (
-    <AnalyticsProvider
-      segmentWriteKey={process.env.NEXT_PUBLIC_SEGMENT_API_KEY}
-      reoDevKey={process.env.NEXT_PUBLIC_REO_DEV_CLIENT_ID}
-    >
+    <AnalyticsProvider reoDevKey={process.env.NEXT_PUBLIC_REO_DEV_CLIENT_ID}>
       <SiteConfigProvider config={config}>
         <MobileProvider>
           <ColorModeProvider>