You can store data by connecting to a database, and you can store logs by either sending them to the system journal and having a daemon collect them, or sending them to whatever cloud you like using a logging library.

It's fine, really. Those database and logging services you can put in a docker if you like, but if you put them anywhere else it works just the same. A Postgres in k8s or a Postgres on a dedicated server is the same as far as the client is concerned.