How do you recover webhooks when your backend is unavailable?

I'm researching how backend teams handle a practical failure case: Stripe, GitHub, or Shopify sends a webhook while your service is deploying, timing out, or returning 5xx.

Do you rely on provider retries, put events into your own queue or DLQ, run reconciliation jobs, or replay by hand? What has actually failed in production?

I'm testing whether a small reliability layer that persists, forwards, retries, alerts, and supports replay would solve enough pain to justify a dedicated tool. This is problem validation, not a claim that the product is proven. Negative answers are useful too.