I've gotten a token for my account, and invoked search with:
https://kagi.com/search?q=<search>&token=<my-token-here>
The result page is blank unless I enable JS. This is contrary to your claims in any case, but specifically breaks textual browsers like "links", which are important to the visually challenged.
I'd expect that such a token-authenticated search would still support a Javascript-less experience.