But practically speaking there's also not much the US can do in that scenario if Russia or China ignores US sovereignty over Mars and sets up their own base. The US's only recourse would be to start a war, and would that be worth it? Sovereignty is more of a practical concept than a legal one: you own what you are both able and willing to defend.

See also the Russian bases in the Australian Antarctic territory. Australia asserts sovereignty over a third of Antarctica, Russia ignores it and sets up bases anyway. Australia has neither the ability nor the desire to fight Russia, so we studiously ignore it.