So you're not under an NDA as you wrote.

I don't know your position but I would assume a NDA is part of your freelancer or employee contract.

In every contract I've ever signed, part of the NDA clause with my employer is that I'm also bound by NDA's my employer is bound by, so if the employer signs an NDA with a customer, I would also be bound by that. It might be worth checking your contract, otherwise having a company sign an NDA doesn't hold much weight if their staff are free to go around sharing the information themselves.

You likely have a confidentiality clause in your contract.

If your company is under an NDA, your company will have an obligation to ensure that you also do not disclose information.

Companies are mostly just collections of people, and an NDA is mostly meant to stop people working on the project from talking about the project.