First step of the Rust router POC. The existing implementation moves unchanged to
litellm/router_backends/python_router.py as PythonRouter, and litellm.Router becomes a
facade that holds it as `backend` and forwards the full current surface, so a Rust
backend can sit behind the same class later. No behavior change.
Tests that override or patch hooks the backend calls on itself now target PythonRouter,
and imports of private helpers and module-global patch strings point at the new module.
litellm-rust/crates/router/POC.md is a hand-off copy of the POC design for sessions that
cannot see the local notes. Delete it before opening a PR.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01VBPzD1X9jBTmKn6ypDQQTY