Christophe above has provided most of the additional structure you need IMHO.
I find that reviewing Github projects helps providing generic folder structures that people are accustomed to.
From my various Confluence templates in addition to the above:
Dev (folders for development)
– this is what you / Christophe have described so far ...
Documentation structure has both objective and subjective aspects. The subjective part is out of scope here. Furthermore documentation depend very much on the methodology. I will therefore propose you a list of general issues you need to consider in all objectivity, rather than a comprehensive answer:
Requirements: choices documentes in /process ...
The original developer is in the best position to write technical documentation, but there are reasons why they wouldn’t:
The developer produces excellent code and rubbish documentation. Then it is better for everyone involved if they spend their time to write excellent code, not rubbish documentation.
Hiring a person to write the documentation may be ...
The question is, do you want to document it as it is now or as it should be?
What I have read from your question is you are thinking about API documentation and not so much user documentation and the code is perhaps not so well maintained and cryptic.
I am afraid if you document now, you will end up throwing most of your work away, once the code is ...
You might want to use a format from which a tool can generate documentation (e.g. as HTML pages) automatically.
For Java code, use Javadoc.
C# uses <summary> XML tags which can be converted by e.g. Sandcastle.
It is important to state what a piece of code wants to achieve.
"The code is the documentation" breaks down if the code actually works ...