Add PostHog, move Plausible to v4, and drop Sentry session replay

PostHog loads after the page is idle through a same-origin /ingest proxy and follows the signed-in Convex user. Plausible uses the per-site script through a /pa proxy. Sentry keeps errors and traces only. Pages load only the @gib/ui modules they import, and client code reads public env from publicEnv.ts so zod stays out of the browser.

apps/next/src/components/layout/header/controls/AvatarDropdown.tsx

@@ -2,6 +2,7 @@
 
 import Link from 'next/link';
 import { useRouter } from 'next/navigation';
+import { resetAnalyticsIdentity, useAnalyticsIdentity } from '@/lib/analytics';
 import { useAuthActions } from '@convex-dev/auth/react';
 import { useConvexAuth, useQuery } from 'convex/react';
 
@@ -23,6 +24,7 @@ export const AvatarDropdown = () => {
   const { isLoading, isAuthenticated } = useConvexAuth();
   const { signOut } = useAuthActions();
   const user = useQuery(api.auth.getUser, {});
+  useAnalyticsIdentity(user?._id);
   const currentImageUrl = useQuery(
     api.files.getImageUrl,
     user?.image ? { storageId: user.image as Id<'_storage'> } : 'skip',
@@ -77,6 +79,7 @@ export const AvatarDropdown = () => {
           <button
             onClick={() =>
               void signOut().then(() => {
+                resetAnalyticsIdentity();
                 router.push('/');
               })
             }