Phase 6: write important school events to the Home Assistant calendar

Add the Home Assistant REST calendar client and the idempotent sync that
writes important school events to Sam's Home Assistant calendar (FR-8). The
school stays read-only; the only write is to the calendar (rule 7).

- internal/calendar: HA REST client (states, create_event, get_events,
  delete_event) and the sync that selects important future events, adopts an
  existing event by its description marker, records the HA event id on the
  item, and records every attempt.
- internal/store: migration 003 (items.ha_event_uid, items.ha_pushed_at and
  the append-only calendar_pushes table), candidates, mark-synced and the
  push log.
- internal/parse: a school event is important; a routine class period is not.
- cmd/school: `school calendar entities|status|push|events`.
- web: an "Add to calendar" item action and a fail-loud calendar banner, so a
  failed write is never swallowed (FR-12).
- scripts/calendar-push.sh, Makefile target, env example, docs and tests.

The target is configurable (SCHOOL_HA_CALENDAR_ENTITY). Home Assistant has no
non-Google writable calendar today, so the entity is asked on AUD-110.

Co-Authored-By: Paperclip <noreply@paperclip.ing>

internal/store/migrations/003_calendar.sql

@@ -0,0 +1,24 @@
+-- Migration 003 — Phase 6 calendar write (AGENTS.md §4 FR-8, §11 Phase 6).
+--
+-- Important school events are written to Sam's Home Assistant calendar. The
+-- write must be idempotent: the Home Assistant event id is stored on the item,
+-- so a re-run updates nothing and never duplicates an event. The push log is
+-- append-only, so a failed calendar write is visible and loud instead of being
+-- swallowed (FR-12).
+
+ALTER TABLE items ADD COLUMN ha_event_uid TEXT NOT NULL DEFAULT '';
+ALTER TABLE items ADD COLUMN ha_pushed_at TEXT;
+
+-- One row per calendar write attempt. ok = 0 with an error is a loud failure.
+CREATE TABLE IF NOT EXISTS calendar_pushes (
+    id         INTEGER PRIMARY KEY,
+    item_id    INTEGER NOT NULL REFERENCES items(id),
+    entity_id  TEXT    NOT NULL,
+    uid        TEXT,
+    ok         INTEGER NOT NULL DEFAULT 0,
+    error      TEXT,
+    created_at TEXT    NOT NULL DEFAULT (datetime('now'))
+);
+
+CREATE INDEX IF NOT EXISTS idx_calendar_pushes_item    ON calendar_pushes(item_id);
+CREATE INDEX IF NOT EXISTS idx_calendar_pushes_created ON calendar_pushes(created_at);