I’m going to give a slightly different suggestion.

You may find it interesting to develop an program without using libc.

Use raw syscalls and make a completely freestanding binary.

This is not as low level as bare-metal but might give you a better understanding of how operating systems work.

You could try writing some core utils replacements

This will only really work on Linux though. Any systems programming language with inline assembly will work fine.

In a way I think being able to derive a formula is a much more valuable skill than rote memorisation, especially in higher education. That being said I’ve also done this when I was just lazy and didn’t remember my lessons…