> The product has absolutely-zero-nada-nothing to do with what my company does
Be careful about declaring your side project unrelated to work. Your definition of unrelated might not match your company’s definition.
If you are programming for your company, and programming for your side project, they’re related at that level at least. I realize they might still be 100% orthogonal, but your employer and the law don’t usually see things the same way you do.
For my last two jobs, I had a side-project before I interviewed, and when it came time to decide on their offer, I had a lawyer write an exclusion for my side-project, legally declaring it unrelated to the company’s business and legally allowing me to moonlight. Getting the lawyer to write it up seemed expensive before I did it, and then seemed like it was both inexpensive and invaluable insurance after I did it. Both companies signed and gave me offers. Asking for the exclusion didn’t seem to hurt my prospects.
On the positive good-news side, you probably are legally in the clear. And also, most companies don’t initiate legal action against employees with side projects. In the few cases I know about where legal action happened, there was more to the story and/or the side project was clearly related to the company’s business.