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/lib/analytics.ts

@@ -0,0 +1,40 @@
+// Analytics event names — single source of truth
+export const ANALYTICS_EVENTS = {
+  BOOKING_STEP_SERVICE: "booking_step_service",
+  BOOKING_STEP_TIME: "booking_step_time",
+  BOOKING_STEP_CONTACT: "booking_step_contact",
+  BOOKING_STEP_SUBMIT: "booking_step_submit",
+  BOOKING_CONFIRMED: "booking_confirmed",
+  BOOKING_ERROR: "booking_error",
+} as const;
+
+export type AnalyticsEventName = (typeof ANALYTICS_EVENTS)[keyof typeof ANALYTICS_EVENTS];
+
+export type AnalyticsPayload = {
+  step?: string;
+  flow?: "public" | "portal";
+  [key: string]: string | undefined;
+};
+
+/**
+ * Fires a lightweight analytics event via window.dispatchEvent.
+ * No-op safe: failures are swallowed so analytics never breaks the booking flow.
+ * Designed for later Plausible/GTM integration.
+ */
+export function fireAnalyticsEvent(
+  eventName: AnalyticsEventName,
+  payload: AnalyticsPayload = {}
+): void {
+  try {
+    window.dispatchEvent(
+      new CustomEvent(eventName, {
+        detail: {
+          ...payload,
+          timestamp: new Date().toISOString(),
+        },
+      })
+    );
+  } catch {
+    // no-op: analytics must never break the booking flow
+  }
+}