Geforce 970 4GB is not good enough to drive anything mildly demanding at 4K due to the lack of sheer processing power and insufficient vRAM (and vRAM on 970 was a big controversy back in the day as it’s actually closer to 3.5GB.
For those unfamiliar, the controversy
surrounds the GTX 970, which breaks
its 4GB VRAM into a 3.5GB chunk of
GDDR5 and a separate 500MB that runs
significantly slower.
Since you’ll be saturating the full GPU memory at 4k easily and often, this will actually manifest as weaker performance on top of everything else. This used to be insignificant in the olden days - most folks were happy with simple 1080p.
The performance at 4k will be mostly limited by the GPU - you will need something stronger here. Perhaps you could get your hands on a GeForce 3070 / 3080? (check your PSU wattage first!) Or wait for 3060ti in Decemeber.
I’d do that first; if you wanted to upgrade to another CPU, that’d also mean, new motherboard and RAM.