The difference between "pets" and "cattle" are that pets have state and need to be taken care of, you can't recreate them from scratch trivially. Cattle are stateless and can be created and destroyed easily.

The whole point of a database is to contain the state - as a pet - so the rest of your application can be stateless - as cattle.

To really get cattle database systems, you need a self-managing cluster architecture that puts things on autopilot like Neon where you've got >=2 copies of each row and can tolerate losing any single box without unavailability.