Chrome can be oddly stubborn about the search provider defaults, and I would not be surprised if you're also running into a quirk or bug with this. In any case, I would add a new Site search entry for Kagi rather trying to edit one of the defaults. (If they bother you, just delete them as I did.)
I like quick shortcuts, so I used 'k' here, but 'kagi.com' is fine, too. (The full URL with https doesn't belong in this field.) Once Saved, I can then set as the default and it'll join Google in Search engines toward the top of the page.
If Kagi isn't my default, I can still simply put focus on the search bar (CTRL+L), invoke my shortcut by typing 'k' followed by tab or space (or just tab, if you set the keyboard shortcut this way at the top of the page) and then enter my query.