fix(bookings): enforce no-overlap atomically via exclusion constraints

Check-then-insert left a race: two concurrent requests for the same
slot could both confirm. Migration 00014 adds three partial btree_gist
exclusion constraints mirroring resourcesCollide semantics (same
staff, same location, both-unassigned), excluding cancelled rows and
class bookings. SQLSTATE 23P01 maps to ErrBookingConflict at all three
write paths so a lost race returns a clean 409.

Validated on a local Postgres 17 container: constraint matrix at SQL
level, repo-level 23P01 detection, concurrent burst yielding exactly
one confirmed booking.

Authored By: TDvorak <[email protected]>

Generated with [Devin](https://devin.ai)

Co-Authored-By: Devin <158243242+devin-ai-integration[bot]@users.noreply.github.com>

apps/backend/internal/db/bookings.go

@@ -2,7 +2,10 @@ package db
 
 import (
 	"context"
+	"errors"
 	"time"
+
+	"github.com/jackc/pgx/v5/pgconn"
 )
 
 func (r *PGRepository) ListBookingsByTenantBetween(ctx context.Context, tenantID string, from time.Time, to time.Time) ([]BookingRecord, error) {
@@ -232,3 +235,11 @@ func (r *PGRepository) DeletePendingReminderJobsForBooking(ctx context.Context,
 	`, bookingID)
 	return err
 }
+
+// IsExclusionViolation reports whether err is a PostgreSQL exclusion
+// constraint violation (SQLSTATE 23P01). The bookings_*_no_overlap
+// constraints raise it when a concurrent request wins the race for a slot.
+func IsExclusionViolation(err error) bool {
+	var pgErr *pgconn.PgError
+	return errors.As(err, &pgErr) && pgErr.Code == "23P01"
+}