Having gone from 1080 to 3070, I think thats a good jump. 3060, is a bit underwhelming. I would look to the 3060ti over the 3060. The price difference of the 3060 to 3060ti isnt much, but the difference between 3060 and 3060ti is like 50% of the difference between 1080 and 3060. The VRAM advantage of the 3060 vs 3060ti is not an issue, mostly because the 3060 doesnt have enough performance to play in the resolutions that need the extra VRAM. 3060 is a 1080p card, 3060ti can play in 1440p. 3070 is a better option, as is the 4060ti, but you need to look for deals.
In the past year, I picked up 2x 3070, one for $250 and the other for $290. A 3060ti for $240 (shipped pricing). Pricing was better during the summer. I still have the 1080, and will throw it in a different build just for fun. 3060 pricing on the used market typically overlaps the 3060ti a good amount (overvalued IMHO), so I think its just better to start looking at the Ti or the 70 unless you have a specific need for more VRAM.
And I did have the 1080 on a z270 platform. Depending on your title, you may see more uplift going to a new platform than with the new GPU. I mostly play Destiny2, and I had little to no change with the 3070 at 1080p, mostly because much of my performance was CPU limited. I could run about 90-110fps at 1080p with low to medium (optomized settings). With the 3070, that was roughly the same. Only that it didnt matter whether I ran 1440p maxed out settings or 1080p optomised settings, the performance was basically identical.
Going to 5600x, it went to 120-140fps range. 5800x3d, I frame limit to 140fps at 1440p and typically see the lowest FPS of 139. This game is not optomised well, but just be aware that depending on the title you may or may not see much of a change in performance. Destiny requires strong single thread performance (5ghz 7700k wasnt enough).