Let me start by giving your student the benefit of the doubt: how might such 'AI characteristics' have arisen?
Words such as 'thus' and 'leverage' are not exactly common in formal and academic writing - which is often far from 'plain English'. A combination of formal phrasing (including passive voice) and 'jargon' may be what students understand to be 'appropriate academic style'. The student may simply be trying to achieve a 'proper academic style' (or 'voice'), perhaps based on (outdated) formal style guidelines or information about the proper connectives in arguments from school (this could well explain 'thus'). Mimicking what one read last is typical for inexperienced writers 'finding their voice' (see, e.g., King, 2010), so it seems reasonable that a student still learning to write 'academically' will mimic one or more of the papers they refer to most.
I also know from my own writing that I go through phases where I use a few words or phrases a lot more than I do at other times, so words used unusually often in one text is not necessarily about generative AI use. It takes more than a few 'characteristic words' to be able to suspect 'this was not written by a human'.
Indeed, that students can try too hard, and produce worse work as a result is not new: Kitching (2008) reported students trying too hard to be properly academic and making their work worse as a result — in this case it was about including a confused theoretical discussion, instead of presenting projects as straightforward empirical work, but I think the point of trying too hard to mimic what is perceived as 'correct' and ending up with something that doesn't 'ring true' as it were remains.
But there are questions you, as a teacher, have to ask yourself. It's clear now that at least some students will use generative AI for written assignments, but there are a number of ways in which they may use it, all with different implications. I saw a presentation (by André Mathe of the University of Bergen) a few months ago where some lecturers in Norway were interviewed about appropriate uses of generative AI. If I remember correctly, it was typically considered entirely acceptable to use genAI for text editing, and even for idea generation, though the lecturers were pretty much in agreement the the first full draft of the assignment should be the students' own work. So for those lecturers, a student drafting an assignment in everyday, informal language, and then uploading to genAI with a prompt along the lines of 'make more academic' would have been acceptable — and an over abundance of words such as 'thus' and 'leverage' (I'm guessing more common in academic texts than anywhere else) could appear.
There are also many things to consider when it comes to exactly why you're inclined to raise the issue to what you suspect may be an AI generated text: a) whether it matters, b) why it matters, c) how it matters, and d) whether (and why and how) it should matter.
But the damage you have done your student and their trust in you and perhaps even other academics, however accurate or inaccurate your questioning of them may have been, should not be underestimated. After all, you have the power.