Phase 6: fix the live Home Assistant write (Local Calendar, no event id)

The first live run against the new calendar.school entity failed loudly twice,
and both causes are fixed here.

- The Local Calendar rejects `return_response` on calendar.create_event. The
  client retries the call without it and ignores the changed-states array that
  Home Assistant returns instead.
- Home Assistant then reports no event id. The item keeps the description
  marker ([compass-nhs:<id>]) as its reference, so it leaves the candidate set
  and is never written twice. The live retry proved it: both events already in
  the calendar were adopted by their markers, with no duplicate.
- calendar.get_events reports `start` / `end` (a date-time or a bare date), not
  `start_date_time`; the reader now accepts all three shapes.

A model must no longer classify events. The calendar write depends on the
school-event rule, and the LLM labelled every event "normal"; events now keep
the deterministic rule under both classifiers.

Also fix the Phase 5 screenshot script: the calendar banner shares the `.scan`
class, so select each banner by its labelled section.

Docs record the accepted decision: Sam chose a Home Assistant Local Calendar,
so the target is calendar.school.

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

internal/calendar/sync.go

@@ -192,17 +192,25 @@ func Sync(ctx context.Context, st *store.Store, c *Client, opts Options, log *sl
 			continue
 		}
 		if uid == "" {
-			// Home Assistant did not report an event id. The marker in the
-			// description still makes the next run idempotent, but say so.
-			log.Warn("home assistant returned no event id; relying on the description marker",
+			// Home Assistant did not report an event id (the Local Calendar does
+			// not answer with one). Use the description marker as the item's
+			// reference, so the item leaves the candidate set and is never
+			// written twice.
+			log.Warn("home assistant returned no event id; using the description marker as the item reference",
 				"item", first.ID, "child", children, "title", first.Title, "entity", c.Entity())
 		}
 		for _, it := range g {
-			if err := st.MarkItemCalendarSynced(ctx, it.ID, uid, now); err != nil {
+			ref := uid
+			if ref == "" {
+				ref = Marker(it.ID)
+			}
+			if err := st.MarkItemCalendarSynced(ctx, it.ID, ref, now); err != nil {
 				log.Error("mark calendar item", "item", it.ID, "err", err)
 			}
+			if _, err := st.RecordCalendarPush(ctx, it.ID, c.Entity(), ref, true, ""); err != nil {
+				log.Error("record calendar push", "item", it.ID, "err", err)
+			}
 		}
-		recordPush(ctx, st, c.Entity(), g, uid, true, "", log)
 		res.Created++
 		created.UID = uid
 		res.Events = append(res.Events, created)