Same essay submitted to two different courses, cross-departmental plagiarism

Caught something unusual this week that our policy doesn’t really address cleanly. A student in my grade 11 world history class submitted an essay on propaganda and media that was, structurally and almost sentence for sentence, the same essay he’d submitted in his English class a month earlier for a completely different assignment on persuasive rhetoric. Different title, tweaked intro paragraph, but the body was nearly identical, likely run through an AI tool once to reframe it for my prompt. I talked to the English teacher and she confirmed the original assignment topic was different enough that this wasn’t an approved cross curricular project, he just recycled his own AI-assisted work and re-skinned it. Our academic integrity policy covers copying someone else’s work and covers AI use broadly but doesn’t say much about a student essentially plagiarizing themselves across two different courses. Curious how other schools handle this. Does self-recycled AI-assisted work even count as an integrity violation the same way, or is it more of a lazy shortcut that needs a different kind of consequence?