Migrate coroutine backend to liblightning

[liblightning](https://github.com/losfair/liblightning) is written in Rust and produces a better result in benchmarks.

Start by reading the rust-coroutines repository and the linked liblightning project to understand the current coroutine backend and the proposed replacement. Compare the existing backend behavior and benchmark claims before deciding the migration scope; done means the library uses liblightning without losing its expected coroutine behavior.

Written by the indexing model from the issue text.