As someone who is nearing the end of their degree and really wants to focus on some inner game engine work, What are some great ways to improve or even test myself within UE5. Curious what everyone has to say on this.

Read and understand its source code.

Going straight to UE5 might be quite a challenge - but there are F.e. ID Tech engines out there, or even such things like ZenGin engine clone, OpenMW, etc. None of these are small - but if you are interested in inner workings of engines, starting with more simple and more specific ones might be good.

Personal opinion - while learning, you should write a small engine (and small game or multiple small games on it + possibly a way to edit something in them visually). Why? Because trying it yourself can often give you more than just reading through the code.