I am in the ACT rather than NSW but principles tend to remain much the same. If anything NSW tends to explicitly codify the minutiae rather more so JT might be able to quote the correct chapter and verse. Anyway, the short answer, I think, is that you are a member of the owners corporation and you can ask to inspect the OC records. Whether they are held by a managing agent or the secretary (if you are self-managed), it is reasonable to book a mutually convenient time.
Perhaps simpler would be to just directly and politely ask for a copy of the things that are pertinent to your concerns. Be open about it. As a member of the OC you have an interest and would like to be reassured by seeing a copy of the engineer’s report and quotes for work to repair … etc. If you have relevant expertise, a non-combative approach might be to offer to assist the committee.
When I was on our committee we would occasionally ask non-committee members with professional expertise to help. Eg. we would sometimes ask an owner with a forestry degree what she thought about a tree someone was worried about before calling an arborist or we would ask an architect owner what he thought about a crack in a wall before getting a builder or structural engineer in. It wasn’t a substitute for professional advice but it helped us to ask the right questions and better understand the answers.