@ushtaritk421 I'm having trouble reproducing this in a clean profile. My steps:
- Create clean profile in Orion
- Open kagi.com
- Login using the Google option (using an existing account)
- Run a search query
Expected result: See search results, stay logged in to kagi.com
Actual result (for me): See search results, stay logged in to kagi.com
Could you try creating a clean profile to test? If it works in that scenario, there might be something going on with your local cookies/cache, which may be resolved by clearing them.
New profile creation: File -> Profiles -> New Profile (use "Clean Profile" template).
Cookie/cache clear for kagi and google: Orion -> Settings -> Privacy Tab -> Cookies & Website Data: Manage -> Search for "kagi", select "kagi.com", click "Remove" button. Search for "google", select "google.com", click "Remove" button. You'll have to re-login to all google login sites.