When creating a custom bang and no "Domain for Snaps" is entered, the resulting saved custom bang/snap will default to "none".

Following the example in the screenshot, searching using @fastgpt
will result in Kagi appending site:none
I expect the snap to default to the domain of the URL (though, a URN option might be cool).
Following the example, I expect @fastgpt
to append site:kagi.com
to my search when no "Domain for Snaps" is specified.