fix(surveys): hold captures until the survey event receiver is hooked

trial_urgency_banner_viewed fires ~1s into the page load and raced the lazy
surveys extension — events captured before its hook exists can never activate
an event-triggered survey (affects real users, not just e2e). capture() now
awaits surveysReceiverReady() (onSurveysLoaded, 3s safety timeout) and runs the
eligibility check after the event has gone through.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

apps/web/src/lib/posthog.ts

@@ -1,7 +1,7 @@
 // PostHog — lazily loaded so it doesn't land in the initial bundle.
 // All exported functions are fire-and-forget; analytics loss on failure is acceptable.
 
-import { resetSurveySession, scheduleSurveyCheck } from "./surveys";
+import { resetSurveySession, scheduleSurveyCheck, surveysReceiverReady } from "./surveys";
 
 type PostHog = import("posthog-js").PostHog;
 
@@ -79,10 +79,13 @@ export function resetUser(): void {
 }
 
 export function capture(event: string, properties?: Record<string, unknown>): void {
-  load().then((ph) => ph.capture(event, properties));
-  // Event-triggered surveys: posthog-js's event receiver sees the capture
-  // above; the debounced check then asks for newly eligible surveys.
-  scheduleSurveyCheck();
+  // Hold captures until the surveys extension's event receiver is hooked (≤3s)
+  // so event-triggered surveys never miss their trigger, then re-check
+  // eligibility once the event has actually gone through.
+  Promise.all([load(), surveysReceiverReady()]).then(([ph]) => {
+    ph.capture(event, properties);
+    scheduleSurveyCheck();
+  });
 }
 
 export function capturePageView(path: string): void {

apps/web/src/lib/surveys.ts

@@ -149,6 +149,25 @@ function show(ph: PostHog, survey: Survey): void {
   notify();
 }
 
+let _readyPromise: Promise<void> | null = null;
+
+/** Resolves once posthog-js's surveys extension has installed its capture hook
+ * (or after a 3s safety timeout). Events captured before that hook exists are
+ * invisible to event-triggered surveys — the trial survey's
+ * trial_urgency_banner_viewed fires ~1s into the page load and was racing the
+ * extension's lazy <script>, so posthog.ts awaits this before every capture. */
+export function surveysReceiverReady(): Promise<void> {
+  if (!ENABLED || typeof window === "undefined") return Promise.resolve();
+  if (_readyPromise) return _readyPromise;
+  _readyPromise = new Promise((resolve) => {
+    setTimeout(resolve, 3000);
+    loadPh()
+      .then((ph) => ph.surveys?.onSurveysLoaded?.(() => resolve()))
+      .catch(() => resolve());
+  });
+  return _readyPromise;
+}
+
 /** Debounced eligibility check — called after captures, route changes and identify. */
 export function scheduleSurveyCheck(): void {
   if (!ENABLED || typeof window === "undefined") return;