I don't know what it is generally considered. I'd guess most would call it a software problem. In my opinion, it is both software and hardware. Here are examples why:

Software: Algorithmic changes to the code (Dall-E vs diffusion models) can give similar results but way faster runtime. The hardware doesn't really change.

Hardware: think about how having custom circuits to run your algorithm (ASICs), or custom chemical processes (brain), can run faster than the same computations occuring on a single CPU or GPU. But your hardware kind of becomes a physical instantiation of your algorithm, from a certain point of view.

These kind of blend together. It is possible that one Algorithm A works best on CPUs or GPUs today and a second Algorithm B takes forever to run on those. But with the correct specialized physical processes (brain), it is faster to run the B than it is A and get the same or better performance. Was it the hardware or software holding it back? You could argue you just needed better CPUs (hardware) for A, or a combination of algorithm B and B-specialized hardware.