Run the tests on Node 22.16, and fix what a fresh setup tripped over

Node 22.16 runs TypeScript only behind --experimental-strip-types (on by
default from 22.18), so `npm test` failed on every file with
ERR_UNKNOWN_FILE_EXTENSION. The flag is harmless on newer versions.

probe and session-diagnose still imported dist/schulcloud/client.js, which
the move to core/ renamed, so both scripts died at import.

A relative MIRROR_DIR broke file serving: res.sendFile refuses a relative
path, and resolveWithin returns an absolute path only when its root is one.
The config resolves it once, at load.

package-lock.json is what `npm install` records today: the `schulcloud`
bin, and no stale peer flags. 101 tests.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

scripts/probe.mjs

@@ -7,7 +7,7 @@
  * Read-only. Usage: `node --env-file=.env scripts/probe.mjs`
  */
 import { loadConfig } from '../dist/config.js';
-import { SchulcloudClient, SchulcloudApiError } from '../dist/schulcloud/client.js';
+import { SchulcloudClient, SchulcloudApiError } from '../dist/core/client.js';
 
 const config = loadConfig();
 const client = new SchulcloudClient(config);

scripts/session-diagnose.mjs

@@ -19,7 +19,7 @@
  * (default 150 — enough to pass the ~2 h mark where an open tab would strike).
  */
 import { loadConfig } from '../dist/config.js';
-import { SchulcloudClient, SchulcloudApiError } from '../dist/schulcloud/client.js';
+import { SchulcloudClient, SchulcloudApiError } from '../dist/core/client.js';
 
 const totalMinutes = Number(process.argv[2] ?? 150);
 const INTERVAL_MS = 10 * 60_000;