It sounds as though the ideal thing would be for her to engage with letterbox, for her sake and the dc's sake, but you contacting her direct is full of risks. It sounds as though the agency isn't much help.
What you could do is contact Family Rights Group or other groups which work with birth families in these situations as they will have experience and may have valuable insights and may be able to provide useful advice which won't put anyone at risk or go against protocols. If you speak to people like this, with the right sort of awareness, then they may provide suggestions. They may know organisations which would make contact with the BM, to tell her about what she needs to do to engage in letterbox and about what organisations that might give support. They may know how to push the agency to do more, if they should be doing more. The BM may not understand her choices. It is impossible to know.
Please keep in mind the MN mantra, do not give of yourself what you cannot afford emotionally, mentally, physically, financially, too.
Vulnerable people have a very skilled way of drawing people into their world I think I see this slightly differently. I think that vulnerable people are vulnerable because they don't have skills, they either don't know the help they need or they don't know how to get it or get it appropriately or place trust where they shouldn't, though some may be manipulative, also that some people who want to help will have poor judgement themselves, and poor boundaries... but there are of course many people who can help vulnerable people, who do have good judgement, are able to recognise manipulation, are able to stay in control, are able to put in place the boundaries they need, and so can help without being drawn into anything.