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>

docker-compose.test.yml

@@ -0,0 +1,31 @@
+# Manual alternative for bringing up the admin tests' database by hand.
+#
+# `npm run test:integration` does NOT use this file: test/integration/setup.ts
+# starts the container directly, because `podman compose` needs a separate
+# compose provider that neither podman nor docker ships, and one container needs
+# no orchestration. Keep the two in step, or delete this file if nobody uses it.
+#
+# Port 3307 and a throwaway data directory on purpose: it must never collide
+# with, or outlive, the dev database from docker-compose.dev.yml.
+services:
+  mariadb-test:
+    image: mariadb:11
+    environment:
+      MARIADB_ROOT_PASSWORD: roottestpassword
+      MARIADB_DATABASE: nachklang_admin
+      MARIADB_USER: nachklang
+      MARIADB_PASSWORD: testpassword
+    ports:
+      - "3307:3306"
+    tmpfs:
+      - /var/lib/mysql
+    volumes:
+      # Applied by the entrypoint on first boot, against MARIADB_DATABASE.
+      # This is the very migration production runs, so a mistake in it fails
+      # the test run rather than the deploy.
+      - ./sql/admin/001_init.sql:/docker-entrypoint-initdb.d/001_init.sql:ro
+    healthcheck:
+      test: ["CMD", "healthcheck.sh", "--connect", "--innodb_initialized"]
+      interval: 2s
+      timeout: 5s
+      retries: 30