!answer bang asks me to login when using a Private Session Link search URL in a new private browsing session

• Use the Private Session Link format https://kagi.com/search?token={MY TOKEN}&q=%s
  to add a custom search engine to Firefox Focus on iOS
• Use the trash icon to completely wipe the browser cookies & state
• Verify the Private Session Link is working by searching for "test"
• Use the trash icon to completely wipe the browser cookies & state
• Search for "!answer how tall is everest"

... and kagi asks me to log in.

If I do a normal search first, then subsequent !answer searches work without having to log in.

I've also confirmed:

• This is different behaviour from the rotten tomatoes bang: !rt test which doesn't ask me to log in.
• The same thing happens on Firefox on Desktop if I open a new Private Browsing session and search !answer test as the first thing I do.

I expected Kagi to show me the Quick Answer search result rather than ask me to log in.