Hi I think improving our usage of doxygen is a good idea. I would start with making a proposal on https://developer.blender.org/ discussing what is wrong currently and what needs to be done to improve things. After that, developers can chime in on what they think and once everyone agrees you can start making changes.
The issue with https://developer.blender.org/T61097 is that we want to make sure to not provide outdated documentation while moving stuff around.
I have answered your questions inline below:
To whom do I ‘sell’ my ideas before starting any heavy lifting?
@ideasman42 has pushed the current Doxygen usage so far. So you would be primarily trying to convince him along with @dfelinto and @jesterKing both act as development coordinators who help push the project in the right direction.
What is the process for claiming such a task, is the bug-tracker used?
Yes, you can claim tasks through
Add Action --> Assign/Claim. The bug tracker is used. I am hoping to create more tasks for the documentation project so newcomers can see better what needs to be worked on.
Where can I see who else is working on this specifically?
No one is really focused on doxygen coverage, besides @ideasman42 and even then it is not his main concern.
What is the normal process with contributions on wiki?
Currently getting access is based on an ask and receive model. If you have a proposal and a clear direction that everyone agrees on, an administrator can give you an account.