Like most people here have already said… That CPU is going to severely bottleneck whatever GPU you get. You could put a 4090 in there, but that would not push frames any faster than, say, a 4060 or 3060 would. In fact, I’d dare to suggest there is not much difference in the 3060 and the 3050 on that rig, compare these two:
There are only two cards that are cheaper than $200 at the moment that are really a deal, the AMD Radeon RX 6600 and the Intel Arc 750, both at ~$199.
If you want a budget card to throw in there that will last quite a long time, you need to up your game. I have heard good things about Intel finally getting their drivers together, so the Arc 770 at $279 is a really solid buy if you are willing to take a gamble, and the AMD Radeon 7600 XT is also not too shabby at $319. Both have 16GB VRAM which means they will last quite a long time, atleast 3 years, possibly longer.
As for system upgrades, you have three options to upgrade core that makes somewhat sense. I fully understand you do not wish to upgrade, but I am going to outline your options anyway because it is way past time. Feel free to ignore the below advice.
El Rico (AM4)
Cheapest core build available today. Not much else to say about it. The 8 core would be a solid boost over the 4790k, and a doubling of RAM is also nice. Still, this system will not last forever. For a cheap budget gaming system in 2024, it is pretty good. However, do not expect it to be exceptional on 1440p / 4k, if you plan to upgrade your monitor soon, I’d look at the other alternatives.
PCPartPicker Part List
El Guapo (Intel 14th gen)
If Intel is your jam, this core will rock your current systems’ socks and knock it thrice around the block. Great upgrade for the price, the only problem is the complete lack of a decent upgrade path. That said, this system can easily keep gaming until AM6 comes out. A great 1440p base.
PCPartPicker Part List
El Inteligente (AM5)
Main idea with this build is that you are upgrading your core now, only to slot in a bigger and more capable CPU later. Pay a little extra now for a really good and cheap system upgrade down the road, so to speak.
Biggest drawback with this build is that you will be spending a bit of your time on a sub-optimal build - but you will have a 50% performance boost with 2 extra cores, quite a bit better than what you have today. You could save $50 on the extra 16GB RAM I suppose, but why bother?
PCPartPicker Part List
Hope that helps, as always, these are just there to outline options, choice is ultimately yours and not pulling the trigger is just as valid of a choice. And yes, the above is also meant for people in a similar situation, even though it may not fit the bill for you specifically.