[Keyserver] Move shared identity client resources to lib.rs

Summary:
Refactor non-endpoint specific items to root of lib.rs.
This is to help with reviewing functional changes later.

Part of https://linear.app/comm/issue/ENG-2764

Depends on D6788

Test Plan:

cd keyserver/addons/rust-node-addon
cargo build

This gets end-to-end tested later

Reviewers: varun, bartek, max

Reviewed By: varun

Subscribers: ashoat, tomek, atul

Differential Revision: https://phab.comm.dev/D6789