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/openapi/bookra.openapi.yaml

@@ -263,6 +263,27 @@ paths:
           required: true
           schema:
             type: string
+        - in: query
+          name: serviceId
+          required: false
+          schema:
+            type: string
+            format: uuid
+          description: Restrict appointment slots to a single service
+        - in: query
+          name: staffId
+          required: false
+          schema:
+            type: string
+            format: uuid
+          description: Restrict appointment slots to a single staff member
+        - in: query
+          name: date
+          required: false
+          schema:
+            type: string
+            format: date
+          description: Return all slots for a single tenant-local day (YYYY-MM-DD) instead of the capped preview
       responses:
         "200":
           description: Availability for a tenant booking page
@@ -270,6 +291,23 @@ paths:
             application/json:
               schema:
                 $ref: "#/components/schemas/PublicAvailabilityResponse"
+  /v1/public/tenants/{tenantSlug}/catalog:
+    get:
+      tags: [Public Booking]
+      operationId: getPublicCatalog
+      parameters:
+        - in: path
+          name: tenantSlug
+          required: true
+          schema:
+            type: string
+      responses:
+        "200":
+          description: Bookable services and active staff for a tenant booking page
+          content:
+            application/json:
+              schema:
+                $ref: "#/components/schemas/PublicCatalogResponse"
   /v1/public/bookings:
     post:
       tags: [Public Booking]
@@ -1270,6 +1308,9 @@ components:
           type: string
           format: uuid
           nullable: true
+        staffName:
+          type: string
+          nullable: true
         locationId:
           type: string
           format: uuid
@@ -1303,6 +1344,42 @@ components:
           type: array
           items:
             $ref: "#/components/schemas/TimeSlot"
+    PublicCatalogResponse:
+      type: object
+      required: [tenantSlug, services, staff]
+      properties:
+        tenantSlug:
+          type: string
+        services:
+          type: array
+          items:
+            $ref: "#/components/schemas/PublicService"
+        staff:
+          type: array
+          items:
+            $ref: "#/components/schemas/PublicStaff"
+    PublicService:
+      type: object
+      required: [id, name, durationMinutes, priceCents]
+      properties:
+        id:
+          type: string
+          format: uuid
+        name:
+          type: string
+        durationMinutes:
+          type: integer
+        priceCents:
+          type: integer
+    PublicStaff:
+      type: object
+      required: [id, displayName]
+      properties:
+        id:
+          type: string
+          format: uuid
+        displayName:
+          type: string
     CreateBookingRequest:
       type: object
       required: [tenantSlug, bookingMode, customerName, customerEmail, startsAt, endsAt]