Overclocking.guide did a nice Thermal Paste Roundup of 47 products last year that included Coollaboratory's Liquid Copper. Their Liquid Copper actually scored poorly compared to the company's LiquidUltra and LiquidPro which actually did very well. In fact, it scored poorly in general.
BTW, it shows LiquidCopper consists of Cooper and silicone, not gallium. The other TIM that said it contained copper did not fair well either and also contained silicone.
I actually don't find this surprising compared to silver based TIM as silver is, by a nice margin a better conductor - even better than gold. But silver easily corrodes and is more expensive than copper. Gold is only used when no corrosion can be tolerated but actually silver and copper are better conductors.
I think the bottom line has pretty much remained the same since the beginning of time. The benefits you get from the most expensive and/or fanciest are usually very little, or even worse than the old standby, Arctic Silver 5 - typically no more than 5°C at the very extremes. And let's face it, if you
need that extra 5°C to keep your system out of the danger zone, stable and from throttling down in speed, then you probably need to address other issues, like cleaning out heat trapping dust, adding an extra case fan, or replacing a failing CPU fan (or getting an AC in your computer room).
More important than which TIM you use is (1) that you use TIM and (2) you apply it properly (which includes thoroughly cleaning any old TIM off the mating surfaces).