I came across an issue that now seems to be present in all my projects. Any normal maps using a procedural texture (such as noise, musgrave, or voronoi) look slightly flat, even on fully smooth-shaded objects. After looking at the normals themselves on an object, I found out that they don't connect at the edges, which seems to be what's causing the flat shading. I still don't know how to fix it however.
I am using Blender 2.93.2. Let me know if any other information is needed.