The feature store has both online / offline components. The offline feature store is used for feature discovery, model training, and batch inference and is backed by Delta tables. You could read/write to offline store from Databricks clusters that support autoscaling . Cost would be a function of the amount of data processed and the complexities of the transformation.
For online stores, in AWS - we support publishing to
- Aurora (MySQL-compatible)
- RDS MySQL
There are different approaches to scale the online stores. Aurora for example supports autoscaling and with RDS, you could add read replicas to scale reads.