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/store/index.ts

@@ -47,7 +47,7 @@ import {
 import { INITIAL_RIVALS } from '@ai-tycoon/game-engine';
 
 export type ActivePage = 'dashboard' | 'infrastructure' | 'research' | 'models'
-  | 'market' | 'serving' | 'talent' | 'data' | 'competitors' | 'finance' | 'achievements' | 'leaderboard' | 'settings';
+  | 'market' | 'serving' | 'talent' | 'data' | 'competitors' | 'finance' | 'achievements' | 'leaderboard' | 'invitations' | 'settings';
 
 export type InfraNavLevel = 'clusters' | 'cluster' | 'campus' | 'datacenter';