feat(GRO-1794): add booking funnel analytics events

- New analytics utility (src/lib/analytics.ts) with ANALYTICS_EVENTS constants
  and fireAnalyticsEvent() – thin wrapper over window.dispatchEvent, no-op safe
  Built for Plausible/GTM integration later.

- Public booking wizard (Book.tsx): fires step-transition events at each step
  (service → time → contact → submit) plus booking_confirmed on the dedicated
  confirmation page.

- Portal BookingFlow (Appointments.tsx): fires equivalent events for the
  portal booking flow. booking_confirmed fires via useEffect when the inline
  success state is shown.

- BookingErrorPage: fires booking_error on mount (no PII in payload).

Events include step name and flow type (public/portal) but contain no PII:
no names, emails, phone numbers, or pet names in any payload.

Co-Authored-By: Paperclip <noreply@paperclip.ing>

src/pages/Book.tsx

@@ -1,6 +1,7 @@
 import { useEffect, useState } from "react";
 import { useSearchParams } from "react-router-dom";
 import type { Service } from "@groombook/types";
+import { ANALYTICS_EVENTS, fireAnalyticsEvent } from "../lib/analytics";
 
 // ─── Types ───────────────────────────────────────────────────────────────────
 
@@ -193,12 +194,14 @@ export function BookPage() {
     setSelectedService(svc);
     setForm((f) => ({ ...f, serviceId: svc.id }));
     setStep(2);
+    fireAnalyticsEvent(ANALYTICS_EVENTS.BOOKING_STEP_SERVICE, { step: "service", flow: "public" });
   }
 
   function goToStep3() {
     if (!selectedSlot) return;
     setForm((f) => ({ ...f, startTime: selectedSlot }));
     setStep(3);
+    fireAnalyticsEvent(ANALYTICS_EVENTS.BOOKING_STEP_TIME, { step: "time", flow: "public" });
   }
 
   function goToStep4() {
@@ -208,6 +211,7 @@ export function BookPage() {
     }
     setFormError(null);
     setStep(4);
+    fireAnalyticsEvent(ANALYTICS_EVENTS.BOOKING_STEP_CONTACT, { step: "contact", flow: "public" });
   }
 
   async function submitBooking() {
@@ -236,6 +240,7 @@ export function BookPage() {
         throw new Error(body.error ?? `HTTP ${res.status}`);
       }
       const data = (await res.json()) as BookingResult;
+      fireAnalyticsEvent(ANALYTICS_EVENTS.BOOKING_STEP_SUBMIT, { step: "submit", flow: "public" });
       setResult(data);
       setStep(5);
     } catch (e: unknown) {

src/pages/BookingConfirmed.tsx

@@ -1,4 +1,11 @@
+import { useEffect } from "react";
+import { ANALYTICS_EVENTS, fireAnalyticsEvent } from "../lib/analytics";
+
 export function BookingConfirmedPage() {
+  useEffect(() => {
+    fireAnalyticsEvent(ANALYTICS_EVENTS.BOOKING_CONFIRMED, { step: "confirmed", flow: "public" });
+  }, []);
+
   return (
     <div
       style={{

src/pages/BookingError.tsx

@@ -1,4 +1,6 @@
+import { useEffect } from "react";
 import { BUSINESS_CONTACT_INFO } from "../lib/contact";
+import { ANALYTICS_EVENTS, fireAnalyticsEvent } from "../lib/analytics";
 
 const STRINGS = {
   heading: "Link Invalid or Expired",
@@ -9,6 +11,10 @@ const STRINGS = {
 } as const;
 
 export function BookingErrorPage() {
+  useEffect(() => {
+    fireAnalyticsEvent(ANALYTICS_EVENTS.BOOKING_ERROR, { step: "error", flow: "public" });
+  }, []);
+
   return (
     <div
       style={{