@LunaLucy2211 There is a new driver for your graphics chip, and it may be enough to install it, along with the other steps you took. (By the way, what did sfc /scannow say when it finished?) Go to the same driver download site you linked, and specifically download "Intel High-Definition (HD) Graphics Driver - Kaby Lake/Gemini Lake." (The other Intel driver is for an older processor/graphics chip, and your laptop doesn't have an Nvidia card.) When you double-click the download, you'll see on-screen instructions for installing.
Restart your computer, and test the game. If it still lags, move your entire Sims 4 user data folder out of Documents\Electronic Arts and onto your desktop, then test again. When you launch the game, a clean folder will spawn with no content, so this is a useful test to see whether there's some issue with your old user data folder.
If you still get lag even in a clean Sims 4 folder, please run another dxdiag.