Heroku posted a post-mortem update: https://status.heroku.com/incidents/2359
We've talked with Vercel, and they've told us that the only way to make notifications work again is by redoing the integration process. To do that, enter the failing Build Trigger in DatoCMS and press the "Authorize Vercel" button again.
Everything is back to normal
Everything is OK now. We'll update this later if one of our hosting partners writes down something on their status pages.
We are closing this issue for now