Thanks for the pointer to inf-clojure. I gave it a try just now, but couldn't get it to connect to my nrepl connection.
But looking at its source I found a solution for my code highlighting issue in the monroe buffer:
I required clojure-mode in monroe.el and then added the following to the define-derived-mode body
(clojure-mode-variables)
(clojure-font-lock-setup)
I don't think inf-clojure knows how to speak the nrepl protocol. I think it uses either the socket repl (that comes with clojure) or stdin/stdout. nRepl is designed for more complex interactions that allow features like goto definition and so on. I think a lot of people use clojure-lsp for that sort of thing these days.
a bit off topic but port's readme has a nice comparison of inf-clojure, port, monroe & cider: https://github.com/clojure-emacs/port#compared-to-other-clojure-tools-for-emacs