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/server/package.json

@@ -15,6 +15,7 @@
   "dependencies": {
     "@ai-tycoon/shared": "workspace:*",
     "@hono/node-server": "^1.13.8",
+    "bcryptjs": "^3.0.3",
     "drizzle-orm": "^0.44.2",
     "hono": "^4.7.10",
     "postgres": "^3.4.7",