Widen booking fetch window, resolve governing booking per-night, add turnover icons/nights to dashboard

Backend:
- fetchBookings() window widened from today-only to yesterday..+7 days, so a
  departing booking (arrived any number of nights ago) and upcoming bookings are
  both in view — the previous today-only fetch couldn't see a departing guest's
  arrival date at all.
- New resolveGoverningBooking(): replaces the single-booking-per-site pick with a
  two-tier resolution — (1) any non-cancelled booking whose stay covers today,
  preferring one not yet marked 'departed' (so a departing guest keeps governing
  blue->purple right up until checkout is confirmed, even with a same-day arrival
  also active); (2) otherwise the soonest upcoming booking, purely for colour
  ('booked' ahead of its own prep window). Also computes booking_kind
  (arrival/departure/stayover), current/total night count, and a has_next_booking
  turnover hint (for departure days with another booking already lined up).
- determineRoomState() no longer forces 'vacant' for a future-dated arrival — that
  case is now handled by resolveGoverningBooking() deciding whether a booking is
  relevant to today at all; once picked as governing it always resolves to at
  least 'booked'.
- zone_state table: new booking_kind/current_night/total_nights/has_next_booking
  columns, persisted every poll alongside room_state and exposed via GET /api/status.

Frontend:
- ZoneCard: room name is now followed by a takeoff (departure) / landing (arrival)
  / bed (stayover) icon plus a current/total nights figure, sourced from the new
  status fields. A departure additionally shows a landing icon when has_next_booking,
  hinting at a same-day turnover before the room's actually marked departed.

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

frontend/src/types.ts

@@ -55,11 +55,21 @@ export interface Zone {
   device_count?: number
 }
 
+// Set alongside room_state from whichever booking currently governs the room (see
+// resolveGoverningBooking() in backend/src/lib/scheduler.js). NULL when today isn't
+// actually one of the governing booking's nights yet (e.g. 'booked' days ahead of
+// its own prep window) or there's no booking at all.
+export type BookingKind = 'arrival' | 'departure' | 'stayover'
+
 export interface ZoneStatus extends Zone {
   room_state: RoomState
   target_temp: string
   last_transition_at: string | null
   last_booking_status: string | null
+  booking_kind: BookingKind | null
+  current_night: number | null
+  total_nights: number | null
+  has_next_booking: boolean
   devices: DeviceSummary[]
 }