feat: calendar hover price tooltip + AvailabilityPage API integration

- Calendar cells: hold mouse 600ms to show price tooltip for that date/room (baseRate + hourly rate if enabled)
- AvailabilityPage: load real categories from API, derive basePrice from room baseRates, fall back to room types if no categories
- Rate periods: persisted to DB via new /api/hotels/:slug/rate-periods endpoint
- New backend migration 021_rate_periods.sql + rate-periods route
- Added api.ratePeriods.{list,create,update,delete} to frontend API client

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/migrations/021_rate_periods.sql

@@ -0,0 +1,15 @@
+CREATE TABLE IF NOT EXISTS rate_periods (
+  id                UUID        PRIMARY KEY DEFAULT gen_random_uuid(),
+  hotel_id          UUID        NOT NULL REFERENCES hotels(id) ON DELETE CASCADE,
+  name              TEXT        NOT NULL,
+  start_date        DATE        NOT NULL,
+  end_date          DATE        NOT NULL,
+  notes             TEXT,
+  category_prices   JSONB       NOT NULL DEFAULT '{}',
+  channel_markup    JSONB       NOT NULL DEFAULT '{}',
+  extra_person_price INTEGER    NOT NULL DEFAULT 0,
+  min_nights        INTEGER     NOT NULL DEFAULT 1,
+  days_of_week      INTEGER[],
+  created_at        TIMESTAMPTZ NOT NULL DEFAULT NOW(),
+  updated_at        TIMESTAMPTZ NOT NULL DEFAULT NOW()
+);