@MissCuddlyBear Unfortunately, your computer's hardware is below the minimum requirements for Sims 4. In particular, the processor and graphics card are both weaker than the minimum, and having only 4 GB RAM isn't helping either. That doesn't mean you can't play, as you've seen, but the computer may struggle with the more demanding packs, of which Pets is one.
Having said that, the driver for your graphics card is quite old, and your dxdiag lists a number of errors related to the driver. So the place to start is by installing a new one. This is the driver download page for your model:
https://support.hp.com/us-en/drivers/selfservice/HP-20-All-in-One-Desktop-PC-series/10734600/model/11955254
Under Driver - Graphics, download the "Intel High-Definition (HD) Graphics Driver" dated January 12, 2018; it's version number is 23.20.16.4849 Rev.A. Even though this driver is a bit old, it's newer than the one you have installed, it should work with your current version of Windows, and Intel doesn't offer anything newer.
If you get an error when trying to install the driver, that's fine, just let me know.