I am also bringing up a relative on a permanent basis and may be in that situation one day. I am also care-experienced and adopted.
I would say let them call your new baby their brother/sister. I think it actually matters little what the legal status is ie. whether you have adopted them (in which case they would legally be siblings) or whether you have them under an SGO or by some other legal order or arrangement. I assume you will be bringing them up until adulthood, and day-to-day and emotionally they will be your new baby's sibling.
Reinforcing that they are cousins could be upsetting insofar as it could feel like undermining the relationship (with you and/or the baby) and also marking them out as different. As someone who was in care, I call the foster siblings I lived with for a long time brother/sister: I only clarify to close friends or if I need to. Likewise, people who call my half-sibling my brother annoy me, as we have always been brought up as full siblings. In both of these cases it is who I was brought up with, and not the legal or biological situation, that was paramount. However, I have always been aware of the legal and biological situation, and of course one or more of the children you care for may come to feel differently. - But from what you've said it sounds like they want/need to call the baby their sibling at the moment.
It is of course important that they are aware of their origins and their own stories, which you already know. This kind of life story work isn't a one-time thing that they will then understand; rather, they will continously be changing and maturing in their understanding of their history and place within your family. It sounds at the moment as though the older ones have anxieties about the new baby and that the younger ones don't necessarily have the grasp yet of the situation. It seems that emphasising that they are all important to you, and all your children, may be quite important to them at present (and looking ahead too).
I know that support for kinship carers is woefully pitiful, and is also often geared towards grandparent carers - who are unlikely to be in this situation - rather than sibling carers. However, there may be some adopters who can point you towards information to help you help your siblings navigate their feelings about their history and place within your family. In answer to your question though, I would say let them call them their sibling, as long as they know, in an age-appropriate way, the biological situation. It can be uncomfortable (I don't know if they ever call you mum - sorry if you mention in your post) - the child I am bringing up still has contact with their mum so it was weird at first when they sometimes called me mummy. However, we let them call us how they like, and in many social situations where the legal situation is not important I'm just mummy.
Hope that helps.
PS I've referred to the children you're bringing up as your siblings for clarity and because that's how you refer to them, hopefully that's ok