@emz_20_02 If you want the best performance this system can reasonably offer, then yes, I'd upgrade the CPU to at least an 8600K, that is if it's reasonably cheap. (An 8400 or 9400 would be a smaller improvement and possibly not worth the price.) If it's currently more money than you'd want to spend, you could hold off for a bit and keep an eye on prices. The faster GPU will have a bigger impact anyway, and you might decide the game runs well enough for you without the CPU upgrade.
What a faster processor does is clear the usual game engine backlog more efficiently. It's not always easy to see when this is happening, but it most often appears when a lot of calculating needs to happen at once. For example, if you own Eco Lifestyle and don't turn off NPC voting, the game will slow down as the votes are tallied and the relevant Neighborhood Action Plans are applied. And then it will (should) go back to running as normal, at least until the next issue.
The other question is whether your power supply has a supplemental PCIe connector. As I mentioned, the 1050 ti and some 1650s don't need one; you'd have to check the specs of the exact model you're buying. (Let me know if you need help with this.) If the PSU does have such a connector, and a 500W unit probably does, then you wouldn't need to worry about this detail, and you could also consider getting a GTX 1060 or 1660 (any flavor) or 2060 if the price is right. Neither is necessary for ultra settings, but you might enjoy the benefits of higher framerates on your 144 Hz monitor.
To be clear, there are two types of "lag" here: delays in rendering and delays in processing. The first is mostly GPU-dependent, and the second is entirely CPU-dependent. Your current CPU is decent enough that I wouldn't expect any major issues with it, not like the GPU where there's a world of difference between the GT 710 and the cards we're discussing here. So you could reasonably skip this upgrade, especially if you're happy with performance once you get the new GPU installed.
I do want to say that a new SSD wouldn't be as much trouble as you might imagine. It would need to be a SATA SSD, which means connecting to the motherboard and the power supply (the latter could probably use the same cable as the HDD does now). Beyond that, reinstalling Windows sounds intimidating but can be done quickly and easily; you only need a USB 3.0 stick you don't mind erasing. Then you either download the chipset drivers from the motherboard's support page, or better yet, you download them beforehand and store them on a different USB for offline installation.
If you're not ready to do that now, keep it in mind as a possible future project. It's the kind of thing you can get right the first time with nothing more than a YouTube guide and some focus.
