You mentioned Horizon Zero Dawn, but now what res or FPS/refresh rate you were aiming for, just max settings.... I assume 1080P? 60FPS min?
I was considering either a RTX 3060 or a RX 5700XT.
Hardware Unboxed did some good reviews on older CPU's and some of the newer GPU's - there was obviously some drop off regardless of GPU, but some of the RTX cards had REALLY pronounced reduction to the point that the new flagships were behind even previous gen mid-range cards (in a handful of examples).
For the purposes of comparison, a 3770K will be at least a few percent lower than a Ryzen 5 1600X (which I think is used in most of the reviews)...
https://www.youtube.com/watch?v=G03fzsYUNDU&t
https://www.youtube.com/watch?v=JLEIJhunaW8
I think you're probably pitching it about right with a RTX3060 although I'd be tempted by a 3060Ti as a max on the RTX side... but honestly, I think that's probably over-spending on a 3rd gen i7.
The appropriate shopping list should be a GTX1060 6Gb (£200-ish), GTX 1070 8Gb (£300-ish) - note NOT the GTX 1060 3Gb (very different card!!).
I think you'd be slightly overspending anything above those, e.g. a RX 5600XT (for ~£400), but if you're spending as much as that, then might as well get something for the "next PC" and as you suggested, go for a
RTX3060 for around £500... RX 5700 XT's are decent cards, but you're competing with miners still and £600 for one of those is just silly, even with an old CPU you'll probably be better off with the RTX3060.
Above that you could double your spend for only marginal increases in performance and your 1% lows (stuttering) will probably still be pretty noticeable.
Please appreciate that patching such an old CPU with a modern GPU is a bit of a journey into the unknown, other than those Hardware Unboxed reviews... I've still got my 3770K, but it's running in my son's "xbox replacement".... with a GTX1050Ti (>60fps on Fortnite on a 60Hz TV) and the only other stuff he plays is Roblox + Minecraft, so we're not asking too much of it!