1. Just do at least 3 searches after logging in to your kagi account on your browser
2. Open menu (for this case Vanadium) - > search engine (under Basics)
3. You can now select Kagi from the list and close settings
The point is to let browser detect Kagi via OpenSearch metadata so you probably should do a few searches from one tab and open another tab to do more.
If these don't work, just re-enter kagi.com in the address bar to start new searches!