I tried Kagi and it is not better than Google or DDG, IMHO not worth any money. I use Google by default and Yandex when I am looking for PDFs, images, repair instructions, pages not indexed by Google at all.
First time I've heard of Yandex. The way you've described it, I might hopefully find it useful for the academic PDFs I've been seeing less and less in Google.
I am not sure about academic PDFs. It is like old google, it searches for keywords, doesn't try any AI guessing what you mean and doesn't blacklist domains like google.