The title is a bit misleading. This is a documentation of current best practices / de factor standards in IRC. It's not a proposal on how to make IRC better.
This project (ircdocs) works in tandem with IRCv3. ircdocs tends to focus on currently-implemented stuff (such as the linked Modern docs), where v3 focuses more on establishing rough consensus around new specifications and features.
Matrix refers to a specification, not an implementation. There is nothing stopping you, or anyone, from implementing a Matrix server in whatever language you'd like. In fact, there is already a server being implemented in Go called Dendrite,[1] another called Ruma[2] that is being implemented in Rust, a "WIP toy" Elixir implementation called Matrex,[3] as well as others.[4]
https://matrix.org/docs/spec/