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>

lib/services/settings.ts

@@ -0,0 +1,32 @@
+import { count, eq } from "drizzle-orm";
+import { db } from "@/lib/db/client";
+import { appSettings, user } from "@/lib/db/schema";
+
+export async function getSetting(key: string): Promise<string | null> {
+  const row = await db
+    .select()
+    .from(appSettings)
+    .where(eq(appSettings.key, key))
+    .get();
+  return row?.value ?? null;
+}
+
+export async function setSetting(key: string, value: string): Promise<void> {
+  await db
+    .insert(appSettings)
+    .values({ key, value })
+    .onConflictDoUpdate({ target: appSettings.key, set: { value } });
+}
+
+export async function getUserCount(): Promise<number> {
+  const result = await db.select({ count: count() }).from(user).get();
+  return result?.count ?? 0;
+}
+
+export async function isRegistrationOpen(): Promise<boolean> {
+  const userCount = await getUserCount();
+  if (userCount === 0) return true;
+
+  const setting = await getSetting("registrationOpen");
+  return setting === "true";
+}