feat(donate): add PostHog analytics events

Track donation lifecycle across form, widget, admin, and backend:
- Form: donation_completed, donation_*_failed, donation_slip_conflict, donation_artifact_conflict
- Widget: donation_widget_displayed, donation_widget_tts_failed, donation_widget_animation_end, donation_widget_connected, donation_widget_heartbeat_failure
- Admin: donation_admin_test_popup, donation_admin_widget_reload, donation_admin_resend
- Backend: donation_widget_state_playing, donation_widget_state_shown, donation_resent

app/widget/donate/api.ts

@@ -3,8 +3,11 @@
 import { db } from "@/lib/db";
 import { donations } from "@/lib/db/schema";
 import { eq } from "drizzle-orm";
+import { getPostHogClient } from "@/lib/posthog-server";
 
 export async function markRunning(id: string) {
+  getPostHogClient().capture({ distinctId: id, event: "donation_widget_state_playing", properties: { donation_id: id } });
+
   await db
     .update(donations)
     .set({ lastPing: new Date() })
@@ -12,5 +15,7 @@ export async function markRunning(id: string) {
 }
 
 export async function markDone(id: string) {
+  getPostHogClient().capture({ distinctId: id, event: "donation_widget_state_shown", properties: { donation_id: id } });
+
   await db.update(donations).set({ sent: true }).where(eq(donations.id, id));
 }