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/migrations/20260812210641_duration_aware_booked_slots.sql

@@ -0,0 +1,84 @@
+-- Follow-up to Phase 2C's final whole-branch review: booked_slots only
+-- recorded (date, time), so availability checking only ever excluded an
+-- exact time match. A 4-hour service booked at 9:00 AM did not block
+-- 11:00 AM or 1:00 PM, even though the two would physically overlap. This
+-- was inert while nothing persisted (Phase 2A/2B); Phase 2C is what makes
+-- it reachable by real customers, so it's fixed before that branch merges
+-- rather than shipped as a known gap.
+--
+-- Fix: booked_slots gains duration_minutes, populated from the booked
+-- service's own duration_minutes at sync time. Availability computation
+-- (client-side, src/data/availability.ts) changes from an exact-time-match
+-- check to a real half-open-interval overlap check: a candidate slot
+-- [candidateStart, candidateStart + requestedDuration) is unavailable if it
+-- overlaps ANY existing booked slot's [bookedStart, bookedStart +
+-- bookedDuration) interval. booked_slots keeps exactly one row per active
+-- booking (not one row per slot-grid-interval it spans) -- the overlap math
+-- lives entirely in the client's pure computation function, matching this
+-- project's established preference for a thin client over new DB logic.
+
+alter table public.booked_slots add column duration_minutes integer not null default 0;
+
+-- The default above only exists so the column can be added without a
+-- backfill value for any pre-existing rows; every row from this point
+-- forward is written by sync_booked_slot() below, which always supplies a
+-- real duration. Drop the default so a future direct insert can't silently
+-- create a zero-duration (and therefore never-overlapping, i.e. bookable
+-- over) row by omitting the column.
+alter table public.booked_slots alter column duration_minutes drop default;
+
+create or replace function public.sync_booked_slot()
+returns trigger
+language plpgsql
+security definer
+set search_path = ''
+as $$
+declare
+  v_duration integer;
+begin
+  if tg_op = 'DELETE' then
+    if old.status in ('confirmed', 'completed') then
+      delete from public.booked_slots
+      where date = old.date and time = old.time
+        and not exists (
+          select 1 from public.bookings b
+          where b.date = old.date and b.time = old.time and b.status in ('confirmed', 'completed')
+        );
+    end if;
+    return old;
+  end if;
+
+  if tg_op = 'UPDATE' then
+    -- Covers both a status change away from 'confirmed'/'completed'
+    -- (cancellation) and a reschedule of a still-occupying booking to a
+    -- different (date, time): either way, the OLD slot may no longer have
+    -- any confirmed/completed booking holding it and its mirror row needs
+    -- to go.
+    if old.status in ('confirmed', 'completed')
+       and (old.date, old.time, old.status) is distinct from (new.date, new.time, new.status) then
+      delete from public.booked_slots
+      where date = old.date and time = old.time
+        and not exists (
+          select 1 from public.bookings b
+          where b.date = old.date and b.time = old.time and b.status in ('confirmed', 'completed')
+        );
+    end if;
+    if new.status in ('confirmed', 'completed') then
+      select duration_minutes into v_duration from public.services where id = new.service_id;
+      insert into public.booked_slots (date, time, duration_minutes)
+      values (new.date, new.time, coalesce(v_duration, 0))
+      on conflict (date, time) do update set duration_minutes = excluded.duration_minutes;
+    end if;
+    return new;
+  end if;
+
+  -- INSERT
+  if new.status in ('confirmed', 'completed') then
+    select duration_minutes into v_duration from public.services where id = new.service_id;
+    insert into public.booked_slots (date, time, duration_minutes)
+    values (new.date, new.time, coalesce(v_duration, 0))
+    on conflict (date, time) do update set duration_minutes = excluded.duration_minutes;
+  end if;
+  return new;
+end;
+$$;