So here is what happened in the meantime. Basically every day, in the backend I would get the warning that the webhook is not existent or configured properly. Simply going to the config module (edit.php?post_type=asp-products&page=stripe-payments-settings#sub), it would in fact find it right away – “Live Webhook Status – Webhook exists”, and upon another refresh the error message on top would go just away by itself.
But today, the webhook has indeed gone missing again, and I had to recreate a new one, and delete the old one in the Stripe dashboard. The test webhook however was still there and fine.
Please, how can this keep happening?