Port generated client crates reorganization to the server

[david-perez]

Unless having a strong reason to deviate (which would probably warrant an RFC), the server generated crates should follow as close as possible the generated client crate reorganization that was laid out in RFC: Client Crate Organization.

[david-perez]

This is blocked by, or should be carried out in tandem with, #2456.

[david-perez]

It's advisable to do #1724 before this.