If I'm not mistaken, it will also react with coppar slightly, but not anywhere close to quickly
The gallium in liquid metal will migrate slightly into the copper, permanently staining it. However, this has no impact on thermal performance and does not compromise the integrity of the copper IHS and/or heatsink. It also doesn't continue indefinitely- the copper will absorb gallium to a certain depth and then stop.*
It does, however, mean that if you just apply once and go, you'll have (VERY VERY VERY) slightly less liquid metal after a few months, and that liquid metal will have (VERY VERY VERY) slightly less gallium and more (indium? tin? idk, ask Thermal Grizzly) than when new.
The upshot is that when using liquid metal on copper, for absolute maximum performance you should
reapply it once or twice after 1-2 month intervals, but once the staining is complete, it'll be stable, and the final (usually second or third?) application of liquid metal should be good for
years.
Not doing so is extremely unlikely to cause any actual damage; however, if you're bothering with liquid metal at all you might as well get the most out of it you can.
*My approximate understanding is that the copper and gallium form a stable complex or alloy of some kind that stops further gallium ion migration from the liquid metal into the pure copper once it hits a certain thickness (several micrometers? half a millimeter? idk), but I'm considerably more vague on the details of the metallurgy than the practical outcome.