Move add table request/response and SerDe to core module

### Description / Background

Split from:
- #7335

We'd like to move the request and response types and SerDe for the REST API add table method to the core module, so that in a future issue we can use them in client code as well as in the REST API implementation.

Locate the REST API add table request and response types and their SerDe, then trace the module boundaries that currently contain them. Move those types and the SerDe into the core module so they can be reused by client code, and verify the REST API still builds and its tests pass.

Written by the indexing model from the issue text.