@emilyffaye Thanks for covering the basic troubleshooting steps and providing all this info. It makes my job a lot easier. You're correct that the CPU use is the most likely culprit, but unfortunately, your laptop's hardware makes addressing that difficult. First of all, the processor is quite weak for Sims 4 even if it's technically over the minimum requirement. So the CPU use will probably always be high, and the question is how much you can bring it down.
The easiest step is of course to run no other apps while you play. The best practice is to restart your computer before launching the game to free up as much RAM as possible (more on that later), and make sure that no apps are set to start with Windows. For that, check the Startup tab, and disable anything you don't absolutely need. You can always run these programs manually.
It can help to put the EA App in offline mode as well. This will probably prevent you from using the Gallery, but you could browse the Gallery in a separate play session, then quit, restart, and play in offline mode when you're ready.
Another issue contributing to the CPU load, perhaps in a major way, is the fact that your laptop has only 4 GB RAM and a very small page file. The low RAM means the processor has to send excess data that would normally be in RAM to the page file, which is a space reserved on the C drive for this purpose. Swapping files back and forth takes CPU resources, and the more memory apps want to use, the more swapping has to happen. This is why I suggested not running anything alongside Sims 4.
On your laptop, this is further complicated by the somewhat small and almost entirely used page file. Normally, I'd show you how to increase its size and leave it at that. But your C drive has only 11 GB free, which is technically enough to prevent storage-related issues, but decreasing that to more like 5 GB could have other significant consequences. So before increasing the page file, please try to free up more space on C, and let me know how much progress you make.