The latest is nvidia driver 570.86.10 which is not “officially” out yet BUT is available on the net (leaked). 565.77 you could try, that one is listed as well in the store.
The iGPU is powerful enough and should handle games too so i dont think that is the issue. Look in nvidia-settings if there is a prime profile and check if your system prehaps has a MUX switch.
As alternative you can try the Pop! OS kernel which is slightly higher (6.9.x) … kinda weird your running into these issues since i game on a RTX 3070 Ti without any issues.