WIP: Use StyledStrings for all REPL prompt customizations

[KristofferC]

This is another version of #51887 (which I didn't know existed until recently) that tries to bring the REPL prompt customization into the post StyledStrings era.

Still need to do some work on it and think about backwards compatbility (some probably needs to be broken) but you can already do something like

using StyledStrings
using Dates
atreplinit() do repl
    # Dynamic prompt with time
    repl.output_prefix = () -> begin
      str = string(Dates.format(Dates.now(), "HH:MM:SS"), "> ")
      styled"{bold,bright_red:$str}"
    end

    # Dynamic prompt with Julia version and styling
    repl.prompt = () -> styled"{bold,magenta:julia v$(VERSION)>} "
end

and get:

This is the native version of https://kristofferc.github.io/OhMyREPL.jl/latest/features/prompt/.

cc @caleb-allen