I’ve experienced this smell, your description is spot on. I don’t know how to help but I’ll share my experience.

I had the smell when I had a copper IUD, Paragard. I had several symptoms that pointed to infection but all tests were negative. Eventually I removed it and all symptoms went away.

This may not be correlated at all, but I’ve read that people with higher levels of copper in their bodies should not use Paragard. I’m just throwing it out there but you could look into low copper diets and possibly zinc supplements.

I think the smegma problem is a separate issue. Unfortunately that’s just gonna happen if you can’t wash with soap.