Notes:
as Tinkeringbell noted in the comments you definitely should reach for help at the institutions you already were in contact with, this is surely not the first case like this
I am not personally anywhere close to a situation like this [ in response to your comment ]
This answer might seem harsh and inconsiderate but I am trying to balance between what you are lawfully allowed to know, what you would like to know and what might be the interests of your siblings
Siblings
I would advice you on viewing siblings more as a sort of 'forced friend', in the sense that you are basically forced to grow up with them and interact with them. Also they are often in the same age group, which makes a kind of 'friendship' easy, although this does not always have to be the case, just as not all friendships last forever.
The only difference to a 'normal friend' is that you also share a lot of things just by being in the same household. Same authority figures, same house, eating together, same festivities, common familiy activities, ...
In your case you share very little. In fact the only thing is that half of your gene pool come from the same creature - your mother. And that is almost meaningless. In fact there is almost no difference in the relationship between you and me, and you and them.
They are total strangers who might have some information you would like to have and thats how I would treat them. At least kind enough to get the information, more if you feel like it.
Your Mothers reasoning
You told us about a letter you have from your biological mother. Without telling its content it creates quite some variance to the situation.
I think the situation depends on why your mother gave you away. She could have done it for a good reason (i.e. to prevent poverty, disease, death, ...) or she could have just regretted being pregnant with you and tried to get rid of you in order to not have to confront her mistakes.
I recommend going through the letter again and trying to figure out why your mother wanted you to never contact her. If she gave a valid reason you might want to let go. A valid reason could be for example that her social environment could pose a threat to hear life if it were to come out that she had another child.
But I think if there was such a drastic part to the story you would have probably told us. If it turns out there actually is such an issue - well bad luck for them. You can't fault yourself for that as it was your mothers job to disclose something like this properly.
So I will guess that it is a minor issue, in which case I tend to recommend you try to arange a meeting via the agency of the institution.
Meeting the people
Before the meeting/What you should be mindful of
remember that these people have not much more in common with you than I do, and you wouldn't assume that we two are going to form a friendship now, so don't expect it from them either
they are likely very different from what you imagine, so keep your expectations low
they are total strangers, so don't trust them more than any other stranger just because you think they are related to you
be aware of what you really want from them and what you are ready to give to them (concerning: relationship, information, maybe even money issues, they might care about inheritance of wealth, ...)
During the meeting
ill have to edit this, give me a moment
If they decline meeting you
Maybe you can still get a couple of your most urgent questions to them through the agency. But don't expect them to react. There is nothing you can do if they don't want to.
You could probably try to push it and just visit them directly but this obviously won't set the relationship at a good start. So just quit it. Accept that these people don't care about you and don't want anything to do with you.
And this might sound fucked up but I don't think there is any shame in it: keep an eye out for any 'family' deaths. You might be entitled to some property.
I also want to take this opportunity and commend your adoptive parents for being open about the adoption. They did exactly what your real parents should have done: be honest about what happened.