[native_rust_library] Cleanup remaining APIs

Summary:
Final part of ENG-6713.

• Moved remaining APIs to submodules
• Fixed some clippy warnings

Depends on D11523

Test Plan: The same test plan for the whole stack: each commit compiles on both platforms. At the final commit (this commit) - played a bit with these APIs, made sure they're callable from JS

Reviewers: varun, michal

Reviewed By: varun

Subscribers: ashoat, tomek

Differential Revision: https://phab.comm.dev/D11524