Switch to Aurora PostgreSQL & Migration Support

I am currently facing issues with my AWS CDK application that has an Aurora Serverless DB cluster running VER_11_13. While trying to restore a backup, I encounter errors indicating that "RDS Extended Support is not available for Serverless v1". Following this, I'm considering switching to a different database engine, specifically Aurora PostgreSQL15_4 but i am unsure how to migrate my data from the V1 to V2 given the roadbloacks.

I would appreciate full migration support in our development environment, as I will be conducting the migration in our production account myself.

You must have demonstrable CDK experience. Please assume this will take 1-2 hours to execute.