Sorry you're having a rough time.
Was this cousin too young to take on 3 children? Maybe losing your three hurt the family so much, they got things together enough for this baby? Framing it that the family were so sad to lose them, but they couldn't care for them, but that they worked really really hard, and could only do this now, and over time, so the cousin could keep this baby?
Why can't you tell them they have a sibling? Or maybe not a sibling, but that BM has had another baby, and that baby is being looked after by x, who couldn't look after you, but is now older/got their act together/couldn't bear to lose another?
They are going to wonder why cousin and gran didn't do the same for them, but you can't change that cousin and gran didn't, and it's not their fault cousin and gran didn't, but they didn't. And they may feel hurt, and angry, and sad, or ambivalent, about that, but they should be allowed to feel that, and deal with it, in the supportive loving setting you provide. I don't think you can keep either the news of the baby, or where the baby lives, from them, I think it's best not to keep secrets, and feel what needs to be felt.
Hard on you, though, so look after yourself.