Add auto-close registration and admin settings page

First user to register automatically becomes admin and registration
closes. Admins can re-open registration from a new settings page.
Uses Better Auth admin plugin for role management and a new appSettings
table for the registration flag. Mobile tab bar now links to settings
instead of inline logout.

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

app/api/registration/status/route.ts

@@ -0,0 +1,7 @@
+import { NextResponse } from "next/server";
+import { isRegistrationOpen } from "@/lib/services/settings";
+
+export async function GET() {
+  const registrationOpen = await isRegistrationOpen();
+  return NextResponse.json({ registrationOpen });
+}