@lanilamb8 I checked about eight different sites and didn't find any 13" laptops that I'd want to recommend. That's not a surprise for gaming laptops—these mostly come with 15.6" screens and up, and the smaller ones are significantly more expensive due to how difficult it is to cool gaming hardware in a smaller chassis. I was a bit surprised to find only one decent non-gaming option smaller than 14", with less storage than is ideal, but perhaps the market has shifted in the last few months.
If 14" is small enough for you, there are plenty of options that could run Sims 4 on medium-high to high graphics settings, although some are clearly better than others. This is the best option I found in terms of price and performance, on sale for $510:
https://www.newegg.com/classic-black-msi-modern-14-c7m-048us-work-business/p/N82E16834156444
These two have the same graphics chip, one that's a bit slower (5-10%, on average) than the chip in the MSI but still reasonably good. The second one has a higher-resolution screen, which may not help with Sims 4—you might have to turn down the in-game resolution to help the game run better—but would be nice for general use.
https://www.bestbuy.com/site/hp-pavilion-plus-14-wide-ultra-xga-laptop-amd-ryzen-5-7540u-16gb-memory-512gb-ssd-tranquil-pink/6550235.p?skuId=6550235
https://www.hp.com/us-en/shop/pdp/hp-pavilion-plus-laptop-14-ey0047nr
The graphics chip in this laptop is a little faster than the one in the MSI, and the screen is also a higher resolution as with the second HP model above. It's very light too, at 2.75 lbs, as opposed to the just over 3 of the HP models and 3.75 of the MSI.
https://store.acer.com/en-us/swift-3-laptop-sf314-512-78jg
This is the only 13" model I found with a similar processor and graphics chip; they're the same CPU and iGPU as in the other two HP models. But this laptop only has 256 GB storage. That's more than enough for Sims 4, which is currently 60 GB with all packs installed, and some saves and custom content. But if you're a cc hoarder, or for that matter if you're going to be working on large multimedia school projects, that might not be sufficient.
https://www.hp.com/us-en/shop/pdp/hp-pavilion-aero-laptop-13-be2047nr
When searching for non-gaming laptops, I only looked at models with 16 GB RAM because it's becoming more and more important these days for Sims 4, especially when the laptop doesn't have a dedicated graphics card with its own video memory. You could get away with 8 GB if you were careful and didn't multitask, and some non-gaming laptops have upgradable memory. So let me know if it's important enough to have a 13" screen to downgrade to less memory and you're not interested in the option above with 256 GB storage. I'll look again and see what else I can find.
For comparison's sake, these are the cheapest gaming laptops I'm seeing at the moment, both 15" and heavier than the ones above. They're essentially the same except for the first one having a slightly older processor and the second having a full terabyte of storage.
https://www.walmart.com/ip/3777161331
https://www.bestbuy.com/site/msi-thin-gf63-15-6-144hz-fhd-gaming-laptop-intel-core-i5-12450h-with-8gb-memory-rtx-2050-1tb-ssd/6559443.p?skuId=6559443
If you have more questions, please feel free to ask.
