I’m beginning a graduate-level probability course shortly and it requires some general knowledge of univariate and multivariate calculus. I’ve never studied it much in a formal sense, so I’m looking for some resources that I could study/review in parallel.

As a learner I do better with intuitive real-world explanations rather than the overly theoretical, if that helps. So far I've mostly looked at Better Explained.

The youtube channel 3blue1brown has some math learning videos, including the Essence of Calculus series. Lots of intuition and great visualizations.

Art of Problem Solving has a calculus text that you might like. I haven't looked at this particular text, but I've used some of their other math books and they're excellent. Their curriculum is focused on practical problem solving and intuition. The book is pricey, but not as expensive as more traditional calculus texts. They have some excerpts you can read to get an idea of their style and approach.

The book description says "Calculus is part of the acclaimed Art of Problem Solving curriculum designed to challenge high-performing middle and high school students. Calculus covers all topics from a typical high school or first-year college calculus course...The book includes hundreds of problems, ranging from routine exercises to extremely challenging problems drawn from major mathematics competitions."