I think OP is right to be cautious. Once given, this information can't be taken back, and things can easily spiral. Even if brother is all chill and good, if it is shared or becomes known by others them the situation can potentially become heightened. Knowing in your own mind that you have a safe place to retreat to is important to your own mental health and wellbeing, and it's good to establish boundaries. Of course, if he was determined enough to covertly follow you home, riffle through your handbag for evidence of a address or stalk your Tesco driver, he could find it out, but moving on the assumption that he is probably just a regular guy, I'm reassuring you that it is perfectly normal to not give this information out at this stage, biological connection or not. It's not about physical safety per se, but also about the mental and emotional safety of knowing that you aren't just opening up your life to someone that you don't really know yet. You might have things that you feel protective over, or just feel you want to go slowly, and that is fine. There is no need to be railroaded into something that can't be taken back.
You have so many things to consider that people who aren't part of adoption might not really know about- how will this impact on any other siblings (bio or adopted) what precedent is being set, what is it like to feel some way obligated to someone you are connected to but don't really know, what complex family dynamics of jealousy, resentment, excitement, frustration are all present in the simple act of giving this information. It's widely accepted that children who are adopted are not frequently in contact with biological parents, which includes not sharing their new address with bio parents. This is often the case even when there is direct contact, so I can understand why this is possibly a very meaningful thing to give. To me, it's almost symbolic, and it's absolutely ok if you don't feel like you are there after so few meetings. If you were in a romantic relationship, nobody would think twice about you waiting to share certain things before certain milestones were met.
With adoption, there is no legal link between siblings post adoption order, and so I suspect technically no obligation to declare for a lower level vetting position. However, if he is fastidious enough to declare everything on his form (which is probably a good idea for him vetting wise), he can only declare what he knows. It also highlights that he has a certain family relationship going in that is potentially going to cause people to be judgemental of him and wade in with many, many opinions and a lack of understanding of the nuanced, complex realities of adoption (see many of the posts above!). If the position is a sensitive one, I would hazard that this might be a theme they want to pursue in terms of interviews, and check that he is able to cope with this appropriately. People can be dicks.... or at least very uninformed. I suspect if it is an open fact that he is adopted/was in kinship care, he will have had to have developed strategies to explain and cope, which might be challenged by a newly forming relationship with a biological sibling-not a bar necessarily, but probably to be aware of. He can just write down that she refused.
Having a biological but adopted sister who won't give her address is hardly a deal breaker though. Plenty of people have family who are far worse are in much higher positions of power. I'm sure plenty of men have had to declare mistresses and criminal acquaintances and "business partners" and illegitimate children that are far more scandalous than simply having an adopted sister who won't give her address yet. Nobody's family is squeaky clean... And I suspect if they are, you might be a bit of a boring person who hasn't had the life challenges to make you truly interesting enough to get some of the reaaaallly good jobs 😂
And as one PP said, to be honest, if it's at a level where it matters that much, they probably already know. Yes, adoption records are sealed. Call me a conspiracy theorist, but I suspect if you are going into MI5, they might have a cheeky gander just in case, you know? So its either high enough that they know and want to see if he is honest (which he is being) or not high enough and it won't matter because they only want to know legally speaking.
OP, my strong suggestion is that you keep your personal details private until such a time as you feel safe and confident, wish him luck with the process and proceed as you originally planned. If he doesn't get the job there's a myriad of reasons why, none of which are your fault. If he does, then good for him. His job is actually not your responsibility. You are well within your rights (both legally and emotionally) to give or not give whatever details you wish and feel comfortable with, or not.
I would consider how you couched the refusal, depending on what you want the relationship to be moving forward, but don't feel bad about it at all. If the recruitment people call and ask, just be honest, but do be aware of scams. I don't know how you could verify that it was actually a recruiter, not just a mate of his though, but that is just my suspicious mind 🤣
Take it slowly and steadily, at a pace you feel ok with.