You are actually better off with the Vega graphics on the TV. 1366x768 is a smaller resolution than 1080p (1920x1080), so you actually gain in gpu power there as the higher the resolution, the harder the gpu has to work.
The cpu outputs fps regardless of resolution, doesn't affect it at all. The cpu might send 100fps to the gpu, it's on the gpu to put all 100 on screen. With 4k that's not going to happen, be lucky to get 10-15. With 1366x768 might get 80. With 1080p might get 60. The gpu still gets 100, but details and resolution decide just how many of that 100 the gpu can finish in 1 second.
Artist can only paint so fast. If all he has to paint is a 2"x2" picture of a red dot, that is quick. If he has to paint a 20ft x 10ft picture from the Sisteen Chapel, that's going to take a lot longer. The longer a frame takes to render, the less frames completed in a second, the lower the fps.
In order to keep a fast paced game like gta5 fluid it requires higher fps. The frames change pretty drastically, pretty fast, so the cpu has to get those to the gpu and the gpu has to get them onscreen asap. The 2200G is a 4c/4t cpu, so is at a disadvantage to start with, has mediocre IPC, no Lcache so relies on system ram. All adding up to mediocre fps no matter what. Add in the igpu which also has to use system ram, system power settings etc and with a high fps demand game like gta5, expect fps to be in the toilet except with seriously low settings.
You can't replace the cpu. The 2200G has an igpu, it's an APU. You have no discrete graphics, only internal graphics, and Ryzen cpus do not have an igpu, only the APU's like the 2200G - 3400G do (that's what the G is for, graphics).