[Keyserver/rust] Used shared identity client

Summary:
Apply shared identity client back to rust-node-addon to
verify that it works. Also cleans up the code quite a bit.

Related to: https://linear.app/comm/issue/ENG-4640

Depends on D8804

Test Plan:

• Run identity service and localstack
• Verify that keyserver can login to identity service upon start

Reviewers: bartek, jon

Reviewed By: bartek

Subscribers: ashoat, tomek

Differential Revision: https://phab.comm.dev/D8820