You can’t have? Or you can’t be sure?
Because you certainly can have. Just because you pay, doesn’t mean they will log your searches. In fact Kagi claim they don’t. And since their only income comes from paying users. If anyone ever found out they’re lying about that, they’d quickly loose a big chink of subscribers and income. As well as get sued for fraud. So it’s rather unlikely they do.

Unlike every other search provider, Kagi is the only one with a business model that ensures it’s users are the customer, not the product. When actually using it every day, that’s quite obvious in the results. Even when you search for a company directly, it’s Wikipedia entry is usually the first result. The the company site is the second.