oh_Cosmos You don't need the Alder Lake patch for an EA App install of Sims 3. EA fixed the issue back in January. So if you've applied the patch since the last time you repaired the game, please repair it again.
Sims 3 does run fine on many newer computers, right out of the box and without any interventions. That's not to say you did anything wrong, only that this should be fixable.
For the issue itself, please provide a dxdiag. Click Windows key-R, enter dxdiag in the run box, wait for the scan to finish, click "Save all information," and save the file to your desktop. From there, you can attach it to a reply using the paper clip (Attachment) icon included with the other formatting buttons.
Generations is not part of the Sims 3 Starter Pack, which includes the base game, Late Night, and High-End Loft Stuff. I don't know why Generations shows up multiple times, but as long as you did only pay for it the one time (as opposed to multiple purchases of Generations alone), don't worry about it.