In cyberpunk I was able to use scaled down resolution and get around 45 fps at 1080p with mixed settings. On the same settings, give or take, same resolution, no RTX and with DLSS I get around 30-45 fps with the 3070. No way that's good. Also, it seems like not matter my graphical settings, I get roughly the same performance.
My cpu usage during cyberpunk is about 85%-95%
You made a contradictory statement where you claimed you used a scaled down resolution (1060), then later the same resolution when talking about 3070.
You are probably using settings that aren't available for 1060 and higher than on the 1060, which is the most plausible explanation.
There is also a thing called "law of diminishing returns", where performance does not increase linearly with more resources.
You state CPU usage is at 85-95%, but maybe not due to the game. You may have some bloatware (or trojan) running in the background. Reinstalling may have gotten rid of it.