Read the timetable from WebUntis

Schulcloud holds the material for a lesson but not the lesson: this school's
course `times` are empty and it publishes the schedule in WebUntis. So "what
do I have today, and has anything been cancelled" was unanswerable, and the
timetable cannot be typed into a prompt either — it changes daily.

core/untis.ts talks to the API the Untis Mobile app uses, and three tools sit
on it: untis_timetable (a day or a range, Entfall, Vertretung, room changes,
the notes on each period, inline homework, the period id), untis_homework (the
class register's list, which is not Schulcloud's tasks) and
untis_lesson_topics (what earlier lessons of a series actually covered, which
is what says where a subject got to).

Read-only, but not by the Schulcloud client's rule: this API is JSON-RPC, so
every call is a POST, reads included. READ_METHODS is the guarantee instead,
enforced at the single choke point and asserted by a test. It matters because
the key can do what the app can — the live account holds W_OWN_ABSENCE, so
the same key could report the user absent.

What the live instance taught us, all recorded in docs/API.md:

- `startDateTime` ends in Z and is local time. The 08:00 lesson reports
  08:00Z, so new Date() would move every lesson by an hour or two.
- A substitution is two periods, the original CANCELLED and the replacement
  IRREGULAR beside it, not one period with a changed teacher.
- Announced tests live in the period's info text. The exam module is unused
  here, so getExams2017 is always empty and that field carries the tests.
- A day with no lessons is not a holiday: the weeks this account spends in the
  company simply have no periods.
- `?v=i3.2` is required, or the call fails with a Java NPE reported as -8998.
  Errors arrive with HTTP 200 and an error member. -8504 is a rejected key and
  -8524 a drifting clock; the tools name both, because no retry fixes either.

Configuration is all four UNTIS_* values or none — three are identifiers and
the fourth is a credential, so a half-filled block is a paste that went wrong.
Without them the tools are not registered at all, since a tool that can only
fail is worse than a missing one. whoami reports the WebUntis identity and
survives a dead Schulcloud session, so "is the server reachable" no longer
gets a misleadingly total no. mcp-env.sh switches WebUntis off for a fixture
run: that key belongs to the real school.

224 tests. All 10 WebUntis smoke checks pass, with a key and without one; the
Schulcloud checks in those runs answer 401 because this machine's session is
logged out.

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

.env.example

@@ -84,6 +84,28 @@ DATABASE_URL=postgresql://schulcloud:schulcloud@postgres:5432/schulcloud
 # file records are immutable.
 # CRAWL_INTERVAL_MS=21600000
 
+# ---------------------------------------------------------------------------
+# WebUntis (optional — the timetable, which Schulcloud does not hold)
+# ---------------------------------------------------------------------------
+
+# Where the school publishes its timetable. With these set, the server offers
+# untis_timetable, untis_homework and untis_lesson_topics, plus the German
+# "tagesvorbereitung" prompt; without them none of that exists. All four values
+# are in one dialog: WebUntis → Profil → Freigaben → Untis Mobile → QR-Code.
+#
+# UNTIS_SECRET is the "Schlüssel" field and is a credential: it authenticates
+# every request as this user, needs no password, works with an SSO login, and
+# stays valid until you generate a new key in that dialog. It can do whatever
+# the Untis Mobile app can — this server only ever calls read methods, by
+# allowlist (src/core/untis.ts). See docs/AUTH.md.
+#
+# Authentication is a time-based code, so the host's clock must be in sync;
+# WebUntis answers -8524 ("invalid client time") when it is not.
+# UNTIS_SERVER=yourschool.webuntis.com
+# UNTIS_SCHOOL=yourschool
+# UNTIS_USER=your.username
+# UNTIS_SECRET=
+
 # ---------------------------------------------------------------------------
 # Limits (optional — sensible defaults are built in)
 # ---------------------------------------------------------------------------