...
Given that Nemesis has likely been around for a while, I would be very surprised if most, if not all of the SC were at least aware of it (& secretive about it). We know they are aware of Outsiders...
I would note that the WC seems to be VERY averse to admitting (even to themselves) the possibility of active conspiracies and covert actions, other than from known agencies (i.e. pre-Changes, they'd readily admit the Ramps had covert actions against them).
I suspect that
individual wizards have noticed Nemfection, but that "the Council" does not admit there is any pattern, or overarching agency. The Senior Council does not discuss it as a body, the Merlin denies it to all & permits no discussion, etc.
I expect the same policy as with talk of a "Black Council," basically.
...
IIRC, Harry mentions looking for Elaine everywhere when he first runs into her in SK. I believe it is only after that endeavor fails that he reaches the conclusion she’s dead...
You're right; I hadn't recalled that scene. That DOES speak to Harry not actually seeing anything happen to Elaine. It's a terrible fire, he fears the worst, but didn't (for example) see a flaming building collapse that he "knew" she was inside. Only after extensive magical searching does he admit to himself that she's dead.
I mean... yes, Harry's psyche often visits Egypt to go swimming, so it's possible that (based on what he saw) any
reasonable person would have concluded she was dead (but Harry, shockingly, wasn't being reasonable).
But Occam's razor says Harry didn't really know, not from seeing it; he feared the worst, and confirmed his fears from extensive magical search.