Add admin identity module: better-auth, per-app permissions, invitations

Introduces src/models/admin/, a dedicated identity and permissions module on
its own nachklang_admin database, and the shared authenticator that feedback
and tickets will move onto in the cutover step. Nothing swaps over yet:
feedback.auth.ts and tickets.auth.ts still authenticate against the legacy
calendar sessions, so production behaviour is unchanged.

- better-auth 1.7 mounted at /admin/auth/*, sessions as httpOnly cookies
  scoped to .nachklang.art so one sign-in covers every *.nachklang.art app.
- Accounts are invite-only: public sign-up is disabled, and the invitations
  plugin is the only code that creates users. Tokens are stored as SHA-256
  hashes and travel in the request body, never in a URL.
- Per-app permissions in user_app_permissions; requireAppAccess(app) queries
  the database on every request (no cookie cache) so disabling a user or
  revoking a session takes effect immediately.
- ADMIN_BOOTSTRAP_EMAIL guarantees a way in on an empty database, idempotently
  and without crashing the API if the database is unreachable at boot.
- Guards prevent an admin from removing their own admin permission, disabling
  themselves, or stripping the last active admin.

The admin pool uses the callback-style mysql2, not mysql2/promise: Kysely's
MysqlDialect drives the pool with callbacks, and the promise wrapper ignores
them, so every query hangs silently. Only the integration tests caught this.

Schema in sql/admin/001_init.sql, derived from getAuthTables() on the
installed better-auth rather than the published CLI, which lags the library
and omits account.issuer.

app.ts is split into src/app.factory.ts so the integration tests drive the
real middleware order rather than a copy of it.

Tests: 131 unit, plus 41 integration tests against a throwaway MariaDB
started by test/integration/setup.ts (docker or podman).

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

src/models/admin/admin.config.ts

@@ -0,0 +1,63 @@
+import * as dotenv from 'dotenv';
+import logger from '../../middleware/logger.js';
+
+dotenv.config();
+
+/**
+ * One place that reads the admin module's environment. Both admin.auth.ts
+ * (better-auth trustedOrigins, passkey origins) and app.ts (CORS) need the
+ * same origin list, and a second parser would drift from this one.
+ *
+ * In production every value is mandatory: a missing BETTER_AUTH_SECRET or a
+ * wrong ADMIN_APP_URL is the kind of misconfiguration that fails as "login
+ * silently does nothing" hours later, so it fails at boot instead. In dev the
+ * localhost defaults below let a fresh checkout run without an .env.
+ */
+
+export const isProd = process.env.NODE_ENV === 'production';
+
+const required = (name: string, devDefault: string): string => {
+	const value = process.env[name];
+	if (value) {
+		return value;
+	}
+	if (isProd) {
+		logger.error(`Admin module: ${name} is not set`);
+		throw new Error(`${name} must be set in production`);
+	}
+	return devDefault;
+};
+
+export const API_BASE_URL = required('API_BASE_URL', 'http://localhost:3000');
+export const ADMIN_APP_URL = required('ADMIN_APP_URL', 'http://localhost:3002');
+
+// 32+ random bytes; better-auth signs cookies and reset tokens with it.
+// Rotating it invalidates every session, which is why it is not derived.
+export const BETTER_AUTH_SECRET = required(
+	'BETTER_AUTH_SECRET',
+	'dev-only-insecure-secret-do-not-use-in-production'
+);
+
+// Passkeys are bound to this: a credential registered for "nachklang.art"
+// works on every *.nachklang.art host, one registered for "localhost" only
+// works in dev. Changing it invalidates every registered passkey.
+export const PASSKEY_RP_ID = process.env.PASSKEY_RP_ID || (isProd ? 'nachklang.art' : 'localhost');
+
+// The apps whose frontends may talk to /admin/* with credentials.
+const parseOrigins = (value: string | undefined): string[] => {
+	return (value || '')
+		.split(',')
+		.map(origin => origin.trim().replace(/\/$/, ''))
+		.filter(origin => origin.length > 0);
+};
+
+export const APP_ORIGINS = parseOrigins(process.env.APP_ORIGINS);
+
+// Kept in sync by construction rather than by three separate lists: the admin
+// app itself always counts, and dev adds the local ports.
+export const ADMIN_ALLOWED_ORIGINS = Array.from(new Set([
+	ADMIN_APP_URL.replace(/\/$/, ''),
+	...APP_ORIGINS
+]));
+
+export const ADMIN_BOOTSTRAP_EMAIL = process.env.ADMIN_BOOTSTRAP_EMAIL || '';