Thesis' "Future Work" section – is it acceptable to omit personal involvement in a mentioned project?
Am I overthinking this?


Yes.


  my examiner is oblivious to the fact that the project that I mentioned in the Future Work section is something that I'm actually working on in a different course. 


Your examiner probably isn't oblivious: Many researchers discuss other works in their future work section, without mentioning that they are already working on them. 


  I'm worried that my examiner will...accuse me of lying...since a project that I'm working on doesn't really count as 'Future Work'.....but does it? 


A project that you are working on is future work, in the sense that it hasn't appeared publicly yet. 

It can be useful to discuss future work without explicitly mentioning that work is already in progress, since such work may never be published, due to unforeseen circumstances, for instance.


  we will be writing a sort of report on our project.


You can cite your  bachelor's thesis in that report.