Just trying to give my take because I was on the same boat.
Had the same CPU, 3600.
Upgraded from 2060 to 3070 ti and on warzone the frames were exactly the same.
I since upgraded to the 5600x and the framerate almost doubled at 1080p, and much stable frametimes and 1% lows, maybe that can be of some help.
My conclusion is that the 3600 is just not good enough to keep up with the 3070 ti.