I can see the option to set a container. But I need to set the public or private option for this container like this… Apple docs

You are absolutely right. I digged deeper into this and found a message on slack from an Apple engineer that suggested to use Core Data for the config and SwiftData for accessing the container. There is a new tutorial video about migrating from Core Data to SwiftData which should also contain some information on how to implement this. Really disappointed to see that Apple is not pushing the shared and public database with this release. I hope for an enhancement release soon...