In interviews I just tell the truth, which is that I'm a consultant, I usually have more than a single client, as otherwise it puts them at risk of me being classed as an employee.

My observations were from how to manage multiple clients together using the extra time from remote work, as the experience is close. The actual mechanics of the moonlighting employee part sounds like a lot of grey to me, but it was common even before covid and I saw it a lot in unionized environments. Typical calls I'd overhear would be people running charities, managing other consultants on other gigs, doing side of the desk startups, etc. It seems pretty normal.