when I make a restriction of access to a type of document for the profile "external project manager", this one has access to all types of documents, which poses problem (confidentiality)
It is because restriction does not hide items by default. It just restricts the list of types (to zvoid users to create items of other types).
If you want to hide items of restricted types, you just have to activate corresponding global parameter (Activity > Control & Restrictions > restriction on types by profile hides items)