the simplicity of Minkowski sums are one of the big reasons capsules are used in collision detection, especially for player models. One of the benefits of this should be the ability to perform collision detection through time, at least with simple primitives.
What I want to try is to collide a bullet (with some speed, represented by a point) and a capsule. A point bullet should also have a simple minkowski representation, and a bullet through time should just be a straight line, a point swept through time. Using this information, we should at least be able to derive the time of impact, which alone should allow for any other collision information we want. Basically similar to something like this: https://blog.hamaluik.ca/posts/swept-aabb-collision-using-minkowski-difference/
What I'm having trouble understanding however, is how to collide with a swept capsule, which itself is a swept sphere. I don't understand how I'm supposed to perform the collision, and I can't find any info online.