how to do aurora schema based sharding?

See if those two are of any use:

https://aws.amazon.com/blogs/database/scale-your-relational-database-for-saas-part-2-sharding-and-routing/

https://docs.aws.amazon.com/whitepapers/latest/amazon-aurora-mysql-migration-handbook/partition-and-shard-consolidation-on-amazon-aurora.html

At last year's AWS re:Invent conference (2023), we announced a "fully managed" sharding solution built on top of Aurora. While it is not quite GA yet, you can get a good feel for the capabilities of it in the YouTube video from the DAT 344 session from that conference. It is an introduction to "Amazon Aurora Limitless Database" and can be viewed at https://www.youtube.com/watch?v=a9FfjuVJ9d8. Please note we are releasing it for Aurora PostgreSQL first with support for Aurora MySQL coming in the not-too-distant future.