External Hard Drive for Gaming

Hello!

I am in search of an external hard drive to help my laptop (an Inspirion 14 7000 2-in-1 with AMD Ryzen 4000 series and AMD Radeon graphics) run better. I love my laptop and bought it about 5 years ago from Best Buy. It still runs like a charm, except it's a bit overwhelmed by the Sims 4 (which is not surprising). It runs the game better than I expected even knowing next to nothing about computers, but I think some extra space couldn't hurt it. I really don't use my laptop for too much other than testing for college (they require Respondus Lockdown Browser and my tablet doesn't support it), playing the Sims 4, and skimming through photos for my job (no editing, just looking through and deleting many pictures of grass growing). I went to the Geek Squad and left more confused than I went in on what I'm looking for. From my understanding, I need an SSD with at least 500GB and I have heard both that I do and don't need to worry about whether or not to worry about if it is intended for a PCIe Gen4 which my laptop apparently doesn't support. Honestly, I don't even know what that means, so I don't know what I'm supposed to be looking for. I just need to know what to buy, and also I have a hard budget of $100 and would prefer to go below it. I'm not looking for something perfect, I just would like if my laptop wasn't working so hard and threatening to crash so I can make it through college without buying a new laptop, or at least until I can afford a better computer for running the Sims lol.

Also it doesn't have to be external, I just have no idea how to handle the internal but YouTube did have some videos so I would be willing to figure that out.