fix: block duration-aware slot overlaps, not just exact time matches

booked_slots previously recorded only (date, time), so availability
checking excluded an exact time match but not a real overlap — a
4-hour service booked at 9:00 AM didn't block 11:00 AM or 1:00 PM.
Add duration_minutes to booked_slots (populated by sync_booked_slot()
from the booked service's own duration) and switch client-side
computeAvailableSlots to a half-open-interval overlap check, also
rejecting candidates that wouldn't finish before closing time.

Claude-Session: https://claude.ai/code/session_01NhxA4npAXAxmCDEJt6kxSH

supabase/tests/database/rls.test.sql

@@ -1,5 +1,5 @@
 begin;
-select plan(47);
+select plan(53);
 
 -- Seed reference data as service_role (bypasses RLS)
 set local role service_role;
@@ -350,5 +350,46 @@ select lives_ok(
   'the unique index can be created after the self-heal dedupe removes the duplicate'
 );
 
+-- Duration-aware booked_slots: the mirror row now carries the booked
+-- service's duration, so client-side availability computation can detect
+-- overlap (not just an exact time match). knotless has duration_minutes = 240
+-- (seeded at the top of this file).
+set local role service_role;
+
+select lives_ok(
+  $$ insert into public.bookings (service_id, date, time, contact_name, contact_phone, contact_email, contact_notes)
+     values ('knotless', '2026-12-01', '9:00 AM', 'Duration Client', '555-0301', 'duration@example.com', '') $$,
+  'confirmed booking for the duration test succeeds'
+);
+
+select results_eq(
+  $$ select duration_minutes from public.booked_slots where date = '2026-12-01' and time = '9:00 AM' $$,
+  $$ values (240) $$,
+  'booked_slots mirror row carries the booked services duration_minutes'
+);
+
+select lives_ok(
+  $$ update public.bookings set status = 'completed'
+     where date = '2026-12-01' and time = '9:00 AM' and status = 'confirmed' $$,
+  'marking the duration-test booking completed succeeds'
+);
+
+select results_eq(
+  $$ select duration_minutes from public.booked_slots where date = '2026-12-01' and time = '9:00 AM' $$,
+  $$ values (240) $$,
+  'booked_slots keeps the correct duration_minutes after confirmed -> completed'
+);
+
+select lives_ok(
+  $$ update public.bookings set status = 'cancelled'
+     where date = '2026-12-01' and time = '9:00 AM' and status = 'completed' $$,
+  'cancelling the duration-test booking succeeds'
+);
+
+select is_empty(
+  $$ select * from public.booked_slots where date = '2026-12-01' and time = '9:00 AM' $$,
+  'booked_slots mirror row is removed after the duration-test booking is cancelled, regardless of duration'
+);
+
 select * from finish();
 rollback;