Planning to start a Bachelor's degree during my PhD: what to say to my advisor?
This is probably more of an opinion answer, but I would say you should say to your advisor either:


  I'm leaving my PhD because _________ and I am going to instead get a bachelor's degree in _______.


or


  I am not feeling good about my research progress and not enjoying research to the point that I am considering leaving the program - can you help?


To be blunt, your plan to do both at once sounds like a horrible blunder. If you are struggling in your PhD now, adding an additional set of responsibilities is not going to make that problem go away. I can't imagine your advisor giving you any different advice than I have.

Further, if you choose to not tell your advisor, I think this would be akin to what is described negatively as "ghosting" in the context of a personal relationship, which is considered to be incredibly rude towards anyone you have an established contact with. Slowly letting your performance decline while you stop paying attention to your PhD and start working on other things is just going to make everyone miserable, and probably destroy any chance you have of getting a good recommendation from your advisor in your future endeavors.

You suggested you've been looking for counseling, and indeed, if your mental health is suffering, that would be a good idea, much better than your plan to take on additional responsibilities.