Also is there any "best practices" for keeping app's user information in sync with Ory and general "I need data from Ory and my database"? Can I enrich Kratos identity with data in registration hook for example? Example use case: User sends message, message need to set an author Id, I'm reluctant to use kratos identity id as a user Id, because there anyway will be 'user meta' table with 'KratosId', 'Profile color', 'etc'. So on the app side I can avoid querring/writing queries that will lookup Kratos Identity -> My user id first, and them work with user data, and just get 'my user id' directly from session.

Yes, webhooks and metadata admin/public should cover that: https://www.ory.sh/docs/kratos/manage-identities/managing-users-identities-metadata#metadata