Added Attachements inside a project do not appear in Documents of the project and vice-versa
It is normal
I consider that Documents and attachements are the same
No, they are completely different

That's why we have designed two different ways to store files
Why does it not work this way?
Attachment are just... attached files (like you may find on emails)
They are attached to an object (ticket, activity, project or else) and cannot be seen elsewhere.
They are not versionned.
Document are files you want to manage in configuration (follow versions).
Then when you create a document, you just define the metadata foir the document.
You attach the files to the versions of the document.
If you want to see both as Documents and on Project, you should not use attachements.
Always use Documents and Document Versions and link Documents (or Document Versions) to the projects.