I've been trying that for a while until I ran out of searches, and was trying to pay - after getting unsolvable captchas thrown at me several times by their payment processor I eventually gave up. Having a captcha at that point also doesn't make any sense at all - as I'm in the EU my card will have to go through strong verification before adding it. For a US audience the experience might be different - I guess that's also their main initial target.
They also just did a bare minimum job of supporting non-javascript - while it nowadays is pretty much impossible to handle payment without allowing some javascript they also have their own account logic unusable without javascript, and they don't have a way to easily open that in a private session when you get stuck. That'd be trivially solvable by just giving you a URL with an account key attached you can paste into a private instance to do your payment.
metager does that way better - they're usable without javascript, and don't force you to create an account with them. You can create a key with tokens tied to it to unlock search features. You can just use that to enable it in other browsers - and you easily jump into a private instance from the key workflow to just add money to the key.
I might revisit kagi later to see if they fixed some of those problems - but for now metager seems to be the best option. I'm a bit amazed they still exist - it was my main search engine back in the 90s before google came around.