Fix: a booking arriving in a few days showed 'booked' instead of 'vacant'

resolveGoverningBooking() was letting an upcoming (not-today) booking govern colour,
so any room with something booked within the 7-day lookahead showed green 'Booked'
regardless of how far off the arrival was. 'booked' should only apply when someone's
actually arriving tonight.

Now a booking only governs state/colour when it covers today (arriving today,
mid-stay, or departing today) — otherwise the room is genuinely vacant. The soonest
upcoming booking (if any) is surfaced separately as vacant_nights, a countdown to
the next arrival, purely informational and no longer tied to colour. Dashboard shows
'Vacant N nights' when something's booked within the window, or 'Vacant 7+ nights'
when nothing was found in the fetched window at all.

New zone_state.vacant_nights column, threaded through saveZoneState/pollOnce/status.js.

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

backend/src/db.js

@@ -108,6 +108,10 @@ export async function initDb() {
       current_night      INT,
       total_nights       INT,
       has_next_booking   BOOLEAN NOT NULL DEFAULT FALSE,     -- turnover hint: another booking follows a departure today
+      -- Only set when room_state = 'vacant': nights until the next known arrival
+      -- within the scheduler's fetch window, or NULL if nothing was found in that
+      -- window at all (displayed as an open-ended "7+ nights" rather than a count).
+      vacant_nights      INT,
       updated_at         TIMESTAMPTZ NOT NULL DEFAULT NOW()
     );
 
@@ -195,6 +199,7 @@ export async function initDb() {
   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 pool.query(`ALTER TABLE zone_state ADD COLUMN IF NOT EXISTS vacant_nights INT`)
 
   await seedDefaults()
 }