For he layperson, probably correct. I’d say thay in a scientific context, the definition needs to be adapted to the research context. What are we looking at, what are we searching for ? How do we define “word” in a usable manner ? Languages are made up anyway !!
I’m afraid I don’t really have specific litterature to recommend, and I’m not quite sure where my notes went ^^’ but I will still recommend a book an categories: “birds colo(u)rs and prepositions”. Not about words per se, but about where and how we draw lines between categories. A more generic approach to the question.

What is a word: Yes.

fun little story: I once visited a lecture called “what is a word?”, and the lecturer started with a quizz presenting… well, pieces of speech and asking whether we would consider it a single word or not. Then they said that barely anyone changes their mind throughout their course, and that the answers would remain pretty much the same at the end 😅 But it was still nice to learn about alllll the theories (there are a lot)