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.bootstrap.ts

@@ -0,0 +1,67 @@
+import * as UsersService from './users/users.admin.service.js';
+import * as InvitationsService from './invitations/invitations.service.js';
+import {sendInvitationMail} from './admin.mail.js';
+import {ADMIN_APP_URL, ADMIN_BOOTSTRAP_EMAIL, isProd} from './admin.config.js';
+import logger from '../../middleware/logger.js';
+
+/**
+ * Solves the empty-database problem: with invite-only accounts and no public
+ * sign-up, a fresh nachklang_admin has nobody who can invite anybody. Rather
+ * than a CLI script somebody has to remember to run against production, the API
+ * makes sure on every start that ADMIN_BOOTSTRAP_EMAIL can get in.
+ *
+ * Idempotent by design - it is safe on every restart:
+ *   - an active admin already exists  -> do nothing
+ *   - the address exists as a user    -> grant it `admin`
+ *   - an open invitation exists       -> do nothing (do not re-mail on restart)
+ *   - otherwise                       -> invite, and mail the link
+ *
+ * Never throws: a database blip at boot must not stop the API from serving the
+ * calendar, feedback and tickets domains.
+ */
+export const bootstrapAdmin = async (): Promise<void> => {
+	try {
+		if (!ADMIN_BOOTSTRAP_EMAIL) {
+			return;
+		}
+
+		const email = ADMIN_BOOTSTRAP_EMAIL.trim().toLowerCase();
+
+		if ((await UsersService.countActiveAdmins()) > 0) {
+			return;
+		}
+
+		const existing = await UsersService.findUserByEmail(email);
+		if (existing) {
+			await UsersService.grantPermission(existing.id, 'admin', null);
+			logger.info('Admin bootstrap: granted the admin permission to the existing bootstrap user', {email});
+			return;
+		}
+
+		// An expired invitation is not "open", so the next restart re-issues
+		// one - which is the recovery path if the first mail never arrived.
+		if (await InvitationsService.hasOpenInvitationFor(email)) {
+			logger.info('Admin bootstrap: an open invitation already exists', {email});
+			return;
+		}
+
+		const invitation = await InvitationsService.createInvitation(
+			email,
+			'Nachklang Admin',
+			['admin'],
+			null
+		);
+
+		const mailed = await sendInvitationMail(email, 'Nachklang Admin', invitation.token, invitation.expiresAt);
+		logger.info('Admin bootstrap: invitation created', {email, mailed});
+
+		// Outside production the Salesforce mail relay is usually off, so the
+		// link is logged instead - that is how a local setup gets its first
+		// admin. Never in production: the log would then hold a live credential.
+		if (!isProd) {
+			logger.info(`Admin bootstrap: ${ADMIN_APP_URL}/accept-invite?token=${invitation.token}`);
+		}
+	} catch (e: any) {
+		logger.error('Admin bootstrap failed', {detail: e?.message});
+	}
+};