Hello there, @AnsleyNevins ...
Unfortunately, I'm not sure that notifications for quiz submissions are even possible. In looking at the "Notifications" screen, there is a row for "All Submissions". But, if you hover your mouse over those two words, you get a little pop-up description that says, "Assignment (except quizzes) submission/resubmission". There are a couple past discussion topics with similar questions:
In the first link, Robbie had provided a response with a link to a Feature Idea. However, that link points to the old Community website, and I tried searching for an updated link to that Feature Idea, but I could not find it. ☹️
Sorry that I don't have better news for you, but I hope this has helped a bit to answer your question. Let us know if you have any other questions about this...thanks!
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