Choose between RTX 4060 / RTX 3060 12GB / RX 6700 XT

If I had to choose a card from those 3 then I would get the 6700XT (again).

4060: I don’t like that 8GB. I use a GTX 1070 8GB on my second (FullHD) PC. The 1070 performance is at minimum “ok” (with Lumen and max everything it’s in an expected range at low FPS). If my game falls below a rate that my 1070 can handle on FullHD it usually even struggles at those szenes on my faster PC in 4K. Anyway with that 8GB the exhausted Ram is getting frustrating (especially if you’ve opened a lot of stuff). So I would not buy any new GPU with 8GB at this time.
3060 12GB: Should “work”. It’s faster than a 1070 but also a bit dated and usually significant slower than the 6700XT.
6700XT: Works fine. I used it for about 2 years on a 4K PC (it’s no 4K card but some games worked in 4K and my UE project did work as well) until I replaced it with a 4070 (which is great). I had issues with drivers from time to time (and kept some more stable version for a while) as many others as well but overall it was good card.