Gamer checking in. Single core performance is very important as games are not quite yet capable of taking advantage of say 12 cores compared to 6 higher performing cores.
It’s why the 5600x3d performs so closely to the 5800x3d while gaming despite it being a 6 core vs 8 core comparison. We encountered something similar a decade ago with i5 vs i7 for gaming games we’re not capable of taking full advantage of hyperthreading. But as time went on the gap between the two widened.
If you don’t do any gaming and don’t plan on buying a dedicated GPU. The 5600g is completely fine as the integrated GPU will take care of all the small day to day desktop tasks.
If you do any gaming get the normal 5600, the extra L3 cache makes a difference in gaming and you won’t be using the iGPU as I imagine you will also pair it with a dedicated GPU.