Add keepalive-status, a log-only session health check

Summarises the running container's keepalive: extension count, latest
budget, transient failures, rejections, restarts.

It deliberately makes no API call. Any authenticated request slides the
session TTL, so a checker that talked to Schulcloud would be sustaining
the session itself and could not report on whether the keepalive is
doing it — the same confound that made the first endurance test
ambiguous. Reading container logs observes without participating.

Warns when the reported budget drops below 7000s, which is the early
signal that extensions have stopped taking effect.

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

package.json

@@ -19,7 +19,8 @@
     "test": "node --test test/*.test.ts",
     "probe": "node --env-file=.env scripts/probe.mjs",
     "smoke": "node --env-file=.env scripts/smoke.mjs",
-    "session-diagnose": "node --env-file=.env scripts/session-diagnose.mjs"
+    "session-diagnose": "node --env-file=.env scripts/session-diagnose.mjs",
+    "keepalive-status": "bash scripts/keepalive-status.sh"
   },
   "dependencies": {
     "@modelcontextprotocol/sdk": "^1.20.0",