I spent a while trying to get eglot to work in inf-clojure-mode, am I right in thinking it doesn't because it's not a source file? Is there a way to get completions in the repl from eglot?

I have no idea about that. Not familiar with eglot

in case anybody is interested, https://github.com/JasonKDarby/inf-clojure/commit/6d761f997627b9d233313e4da4e896d53fa595dc. It's useful for things like embedded shadow-cljs where a clj repl (not sure on the verb here) 'becomes' a cljs repl so you don't need to try to update inf-clojure's repl type. I just started using it so I'll try it out for a while before making a pr

You will not get eglot completions in the repl. The buffer needs to be associated with a clojure file that clojure-lsp can perform analysis on.