Render API documentation on the website

[fsimonis]

We should render the API on the website, including bindings:

Language	Status	Where	How
C++	done	https://api.precice.org/cpp	Doxygen
C	done	https://api.precice.org/c	Doxygen
Fortran (C implementation)	done	https://api.precice.org/fortran	Doxygen as C functions, Fortran module not available
Fortran Module	missing		Doxygen
Python	done	https://api.precice.org/python	via sphinx (autodoc for cython)
Rust	barebone	https://api.precice.org/rust forwards to docs.rs	via cargo rustdoc
Julia	missing		documenter.jl
Matlab	missing		?

edit: updated the table

[MakisH]

Trying to fill the boxes with some additional search:

• For Julia, there seems to be Documenter.jl with some examples.
• For Matlab, there seems to be a Sphinx extension. Note that the MATLAB bindings also use C++ as a bridge.

[MakisH]

Interesting: The NumPy project seems to be using Breathe to render Doxygen in their Sphinx website: https://www.breathe-doc.org/

(from an SSE student presentation)

[fsimonis]

I patched the rust bindings and they now build on docs.rs (automatically picked up).