There is still debate going on as to whether you should be running your database services in containers—this has pretty much been around since Docker first started to get traction, and unfortunately, there is no simple yes or no answer.
Whenever I approach a project, I tend to look at the usage and what impact the database has on the overall performance of the application itself, and then work back from there.
Kubernetes allows you to run a PetSet; think back to the pet versus cattle analogy from the start of the book. In Kubernetes v1.5, as the feature left alpha, it became known as a StatefulSet. The feature came out of beta in Kubernetes v1.9.