https://en.wikipedia.org/wiki/United_States_Space_Surveillan...
Much as the US is aware of the orbits of their satellites.
If you already assume that it's hard to 'hide' the existence and orbits of your satellites from an advanced observer with good telescopes and ground radar and ways of correlating the data, the fact that your ocean surveillance satellites emit radar might not be a problem. No need to be passive about it.
There isn't much need for stealth in all this the same way there isn't for an optical spy satellite. The adversary knows it is there and what it is looking at. The adversary just doesn't know its exact capabilities, and there's not much they can do about it being up there that doesn't lead to a sudden military escalation of some kind.