When guests check out through Hospitable, you cannot fire a GA4 purchase event from your own site’s tag container.
Why this happens. The booking confirmation happens on Hospitable’s domain, not on your site.
What can run on your site. Two events can fire from your site: search_availability when a guest submits dates in the widget, and begin_checkout when the guest moves to the booking step. You can push both through the dataLayer for Google Tag Manager.
Tracking purchases. For purchase attribution, use a server-side path that reads from Hospitable’s reservation data. For example, a Zapier automation can receive the reservation and send the event to GA4.