This looks more like a Zapier connection scope issue than a Zoom recording limitation. For Zapier to trigger across the org, the Zoom connection needs shared access permissions, and Zapier also says the admin must add the affected users to the Zapier app. Without those two pieces, the New Cloud Recording trigger can end up firing only for the connected owner account.
If you continue having issues with Zapier and are considering building your own recording and meeting automation, Recall’s Meeting Bot API is a great place to start.
I even tried to use the basic Webhook app in zoom itself and it still doesn’t trigger on recording.completed which I suspect is happening to the Zapier app’s webhook as well.