Either I wasn't clear enough or you misunderstood. I'll try to explain again in detail.
Kagi Search Beta as an inbuilt search engine. However, it cannot be used without login to Kagi search. So to use Kagi search, one has to login to Kagi, but that login credentials data is linked with other browsing data.
I frequently clear browsing data. Every time I do that, this Kagi login credentials is also cleared along with rest of the browsing data.
If I have to login everytime I clear data, it defeats the purpose of an inbuilt search engine.
So I was suggesting to separate the data storage for search engine credential with the rest of the browsing data.
Both should have separate options for clearing data.
Or, an alternative that I propose is, along with all the options already provided in
Clear Browsing Data menu option, an additional option
Kagi credentials can also be added.