@TheSierraJ1 That laptop should be able to handle Sims 4 on medium settings, but that's probably about it, unless you don't plan on installing some of the more demanding expansions. While its processor is quite powerful in its class, its integrated graphics chip is not at all, and the graphics chip would be the limiting factor.
Is there a particular reason you want an i7 CPU? The i5-10300H equals or surpasses the i7-1065G7 in benchmark tests, and it has the same number of cores and threads. More relevantly, it comes in laptops that also have a dedicated graphics card, one that can run Sims 3 on ultra settings. And there are plenty of laptops with a 10300H and an Nvidia 1650 for under $800. The 1065G7 will also be rated by Sims 4 as low or maybe medium because of its low base clock speed, which will affect some of the game's default options and may have other in-game effects as well. You could manually rate your card higher though.
If you really want an i7 and would like a gaming laptop, this is the only one I saw for under $800:
https://www.walmart.com/ip/545386564
I don't know as much about the brand, but it's supposed to be overall fine, about the same as other standard gaming laptops. This model also comes with 16 GB RAM, unlike most in this price range.
If you're not committed to getting an i7, there are plenty of options with an i5-10300H, for example these two:
https://www.bestbuy.com/site/acer-nitro-5-15-6-laptop-intel-core-i5-8gb-memory-nvidia-geforce-gtx-1650-256gb-ssd-obsidian-black/6413247.p?skuId=6413247
https://www.newegg.com/top-cover-shadow-black-keyboard-deck-shadow-black-logo-green-chrome-hp-pavilion-16-a0025nr-gaming/p/N82E16834272462?Item=N82E16834272462
They don't have as much storage as the HP though. These two have a 512 GB solid state drive; the first has a slightly weaker (but still more than fine for Sims 4) 9300H:
https://www.newegg.com/obsidian-black-acer-nitro-5-an515-54-599h-gaming-entertainment/p/N82E16834316959?Item=N82E16834316959
https://www.newegg.com/obsidian-black-acer-nitro-5-an515-55-55sd-gaming-entertainment/p/N82E16834316951?Item=N82E16834316951
There's also this option, with 16 GB RAM and a much faster Nvidia RTX 2060, which is significant overkill for Sims 4. It has a 256 GB SSD and a 1 TB mechanical drive in case you need the extra storage, and it's somehow $790 at the moment. I'm guessing it's a temporary Black Friday sale.
https://www.walmart.com/ip/480990436
If you have more questions, please feel free to ask.