That’s basically what is done all the time in languages where monkey patching is accepted as idiomatic, notably Ruby. Ruby is not known for its speed-first mindset though.

On the other side, having a type holding a closed set of applicable functions is somehow questioning.

There are languages out there that allows to define arbitrary functions and then use them as a methods with dot notation on any variable matching the type of the first argument, including Nim (with macros), Scala (with implicit classes and type classes), Kotlin (with extension functions) and Rust (with traits).

Yes, language design is a hugely important determinant of interpreter or JIT speed. There are many highly optimised VMs for dynamic languages but LuaJIT is king because Lua is such a small and suitable language, and although it does have a couple difficult to optimise features, they are few enough that you can expend the effort. It's nothing like Python. It's not much of an exaggeration to say Python is designed to minimise the possibility of a fast JIT, with compounding layers of dynamism. After years of work, the CPython 3.15 JIT finally managed ~5% faster than the stock interpreter on x86_64.