I ran what you suggested and it freed up quite a bit of space and flagged a number of issues that it fixed. I do not see any immediate effect, but I suppose it is good to keep things tidy.
The files I submitted in my original post were designed that way to make the problem I'm seeing as evident as possible. It is still a problem, although less obviously so, in other scenarios. My previous files that I created had way more stuff going on, so I am not sure how comparable they would be.
Funnily enough, your response was enough to make me take a slightly different approach to my fault tracing and I think I have narrowed things down a bit. I have done a majority of my previous work in 8 bit colors. For this piece I was about to start working on I knew there would be a lot of focus on skin tones, so I switched to 16 bit colors in order to enable smoother transitions and make it look realistic. As I was starting off I wanted to make my own gradient through brushing, so I started with a very dark background and wanted to gradually brighten it through brush strokes, which is when I discovered the very dark banding as I showed in my original post. I couldn't look past it as it was so disturbing to my eyes.
Today I opened one of my old files that i finished some time ago, sRGB 16 bit, and tried converting it to 8 bit instead. To my surprise I couldn't see a single thing changing. I toggled between undo and redo for a while but there was no change whatsoever. I then proceeded to create gradients (using the gradient tool) from black to white in two new documents, one 8 bit and one 16 bit. The 8-bit version actually looks better, because it applies dithering which the 16-bit does not. I am not sure really what's going on at this point.
For now, I will continue to work in 8-bits, because I think I can adapt so that it suits my needs. But I am still confused as to why I see no improvement from working in 16-bit. The way I understood it is that you get a way wider color range at your disposal but it will make your files larger and heavier to work with. Do you have any theory as to why I am experiencing this? Does it make sense to you at all?