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>

backend/src/db.js

@@ -99,6 +99,15 @@ export async function initDb() {
       room_state         TEXT NOT NULL DEFAULT 'vacant',   -- vacant | booked | heating_up | occupied | cooling_down
       last_booking_status TEXT,
       last_transition_at TIMESTAMPTZ,
+      -- Dashboard's takeoff/landing/stayover icon + night-count, computed alongside
+      -- room_state from whichever booking is currently governing the room (see
+      -- resolveGoverningBooking() in lib/scheduler.js). NULL when there's no booking
+      -- whose stay actually covers today (room_state 'booked' from a future arrival,
+      -- or 'vacant').
+      booking_kind       TEXT,                              -- arrival | departure | stayover | NULL
+      current_night      INT,
+      total_nights       INT,
+      has_next_booking   BOOLEAN NOT NULL DEFAULT FALSE,     -- turnover hint: another booking follows a departure today
       updated_at         TIMESTAMPTZ NOT NULL DEFAULT NOW()
     );
 
@@ -182,6 +191,11 @@ export async function initDb() {
   await pool.query(`ALTER TABLE zones ADD COLUMN IF NOT EXISTS ac_vacant_setpoint NUMERIC(4,1)`)
   await pool.query(`ALTER TABLE zones ADD COLUMN IF NOT EXISTS ac_vacant_fan_speed TEXT`)
 
+  await pool.query(`ALTER TABLE zone_state ADD COLUMN IF NOT EXISTS booking_kind TEXT`)
+  await pool.query(`ALTER TABLE zone_state ADD COLUMN IF NOT EXISTS current_night INT`)
+  await pool.query(`ALTER TABLE zone_state ADD COLUMN IF NOT EXISTS total_nights INT`)
+  await pool.query(`ALTER TABLE zone_state ADD COLUMN IF NOT EXISTS has_next_booking BOOLEAN NOT NULL DEFAULT FALSE`)
+
   await seedDefaults()
 }