As a hobbiest with trying to learn what exactly would a bench oscilloscope do for me?
One important benefit for you as a beginner is that you will be able to debug issues with grounding and insufficient decoupling of the voltage rails in your circuits. These are very common mistakes, and without an oscilloscope you can simply not find the problems - when you measure your voltage with a multimeter, it might look fine.

As far as I can see, your DSO138 only has one channel. Any real oscilloscope will have at least two channels, which means that you can compare two signals: how it looks like before you put it through a circuit you have built, and how it looks like after your circuit. This will give you a lot of insight into potential problems with your circuits, especially when you are trying to learn electronics.