Add auth system with invite-only registration and admin roles

JWT-based auth (hono/jwt + bcrypt), anonymous-first flow preserved.
Registration requires invite code when REQUIRE_INVITE=true. Admin
user seeded on startup (admin/admin, forced password reset). Login
accepts email or username. Admin invitations management page in
sidebar. Regular users get invite-a-friend button when USER_INVITATIONS > 0.
Frontend gate screen blocks game access for unregistered users with
invite code entry, registration, login, and password reset flows.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

apps/web/src/App.tsx

@@ -3,10 +3,30 @@ import { useGameStore } from '@/store';
 import { MainLayout } from '@/components/layout/MainLayout';
 import { NewGameScreen } from '@/components/game/NewGameScreen';
 import { OfflineCatchUp } from '@/components/game/OfflineCatchUp';
+import { InviteGateScreen } from '@/components/game/InviteGateScreen';
 import { useGameLoop } from '@/hooks/useGameLoop';
+import { useAuthGate } from '@/hooks/useAuthGate';
 import { TICK_INTERVAL_MS } from '@ai-tycoon/shared';
+import { Sparkles } from 'lucide-react';
+
+function LoadingScreen() {
+  return (
+    <div className="min-h-screen flex items-center justify-center bg-gradient-to-b from-surface-950 to-surface-900">
+      <div className="text-center">
+        <div className="inline-flex items-center gap-2 mb-4">
+          <Sparkles className="text-accent-light animate-pulse" size={32} />
+          <h1 className="text-4xl font-bold bg-gradient-to-r from-accent-light to-accent bg-clip-text text-transparent">
+            AI Tycoon
+          </h1>
+        </div>
+        <p className="text-surface-500 text-sm">Loading...</p>
+      </div>
+    </div>
+  );
+}
 
 export function App() {
+  const { loading: authLoading, needsInvite, needsPasswordReset, setRegistered, setNeedsPasswordReset } = useAuthGate();
   const companyName = useGameStore((s) => s.meta.companyName);
   const lastTickTimestamp = useGameStore((s) => s.meta.lastTickTimestamp);
   const [catchUpTicks, setCatchUpTicks] = useState<number | null>(null);
@@ -23,7 +43,22 @@ export function App() {
     }
   }, [companyName, lastTickTimestamp, catchUpDone]);
 
-  useGameLoop(!catchUpDone);
+  useGameLoop(!catchUpDone || authLoading || needsInvite || needsPasswordReset);
+
+  if (authLoading) {
+    return <LoadingScreen />;
+  }
+
+  if (needsInvite || needsPasswordReset) {
+    return (
+      <InviteGateScreen
+        onRegistered={() => {
+          setRegistered(true);
+          setNeedsPasswordReset(false);
+        }}
+      />
+    );
+  }
 
   if (!companyName) {
     return <NewGameScreen />;