But you could say the same for any code that say, touches the filesystem.

I meant that the code has to be deployed to a separate system.

Application code that touches the file system is still deployed along with the application code.

You might commit schema.sql into your application repository, but that's not the state of your database.

I think you are confused. A PG extension is code like any other. For the use cause such as partitioning you should not need to create any schema, what you are doing would be to write a code that acts on schema.

Schema usually is needed for application that will be using a database. I also don't understand the scare about using schema. Schema is FAR FAR FAR simpler to deploy than a Java application.