If you sign up with a masked address then they only have that. You can likely sign up for more than once if you’re needing a new pool of searches, though obviously paying for searches might out you.

I did a bit of comparison… they’re at LEAST using Google and Bing, probably a couple more. I tested with searches I’d already done outside of Kagi and it identified most of the relevant results I’d had to ID across multiple engines before. I do think the price is ah, pricey though, and I’d want more info before I used it for sensitive stuff.