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/admin/settings/route.ts

@@ -0,0 +1,30 @@
+import { headers } from "next/headers";
+import { NextResponse } from "next/server";
+import { auth } from "@/lib/auth/server";
+import { getSetting, setSetting } from "@/lib/services/settings";
+
+export async function GET() {
+  const session = await auth.api.getSession({ headers: await headers() });
+  if (!session)
+    return NextResponse.json({ error: "Unauthorized" }, { status: 401 });
+  if (session.user.role !== "admin")
+    return NextResponse.json({ error: "Forbidden" }, { status: 403 });
+
+  const registrationOpen = (await getSetting("registrationOpen")) === "true";
+  return NextResponse.json({ registrationOpen });
+}
+
+export async function POST(request: Request) {
+  const session = await auth.api.getSession({ headers: await headers() });
+  if (!session)
+    return NextResponse.json({ error: "Unauthorized" }, { status: 401 });
+  if (session.user.role !== "admin")
+    return NextResponse.json({ error: "Forbidden" }, { status: 403 });
+
+  const body = await request.json();
+  if (typeof body.registrationOpen === "boolean") {
+    await setSetting("registrationOpen", String(body.registrationOpen));
+  }
+
+  return NextResponse.json({ success: true });
+}