feat(booking): stepped public booking flow with service/staff selection

The public booking page showed a capped flat preview of slots with no way
to pick a service, day, or staff member. Replaces it with a stepped flow:
pick service, optional staff preference, pick a day, pick a time.

Backend: availability accepts serviceId/staffId/date filters (default
response unchanged for the embed widget), a new public catalog endpoint
exposes bookable services and active staff, and slots carry staffName.
Slot generation and booking creation now honor tenant-wide and per-staff
blocked days; appointment requests must fit inside a matching
availability rule and reference tenant-owned, active staff and locations.

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

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

apps/backend/internal/domain/models.go

@@ -114,6 +114,7 @@ type TimeSlot struct {
 	ServiceID         *string `json:"serviceId,omitempty"`
 	ClassSessionID    *string `json:"classSessionId,omitempty"`
 	StaffID           *string `json:"staffId,omitempty"`
+	StaffName         *string `json:"staffName,omitempty"`
 	LocationID        *string `json:"locationId,omitempty"`
 	StartsAt          string  `json:"startsAt"`
 	EndsAt            string  `json:"endsAt"`
@@ -129,6 +130,24 @@ type PublicAvailability struct {
 	Slots      []TimeSlot `json:"slots"`
 }
 
+type PublicService struct {
+	ID              string `json:"id"`
+	Name            string `json:"name"`
+	DurationMinutes int    `json:"durationMinutes"`
+	PriceCents      int    `json:"priceCents"`
+}
+
+type PublicStaff struct {
+	ID          string `json:"id"`
+	DisplayName string `json:"displayName"`
+}
+
+type PublicCatalog struct {
+	TenantSlug string          `json:"tenantSlug"`
+	Services   []PublicService `json:"services"`
+	Staff      []PublicStaff   `json:"staff"`
+}
+
 type CreateBookingRequest struct {
 	TenantSlug     string  `json:"tenantSlug"`
 	BookingMode    string  `json:"bookingMode"`