Off the bat, case studies seem more in depth and include proposed solutions and redesigns, whereas usability tests just seem like an analysis of the UX of an app. Do I have that right? If so, are usability tests good to showcase on your portfolio if you're just starting out, considering they're not as "in-depth"?
You seem to misunderstand what case studies and usability tests are for.
Case studies are meant for finished products; you analyze the way the product is used and by whom. You define problems, pain points, task flows, and ultimately the ways the product addresses these. As you can tell from the description, case studies are great for showing a design process, the thoughts behind it and how solutions were made. This makes it a valid part of a portfolio redesign piece.
Usability tests are for iteration; you test designs with users to determine whether or not your product is matching user needs and expectations. It’s a tool used to further tweak user flows to make it more user friendly. Unless you made your own redesign and want to test this, it doesn’t lend itself as a stand-alone portfolio piece.
If you’re looking to analyze designs for portfolio pieces, consider doing case studies with a redesign proposal.