No this is wrong and a security issue. Thank you for the context I was not at Kagi in August yet.
The page may have mixed content in which it shows https but the website is not secure, for example https://very.badssl.com/

Also desktop shows the padlock with full url to me.
Browsers nowadays went away from showing the lock icon for securite sites completely so maybe we can consider it and show it only on insecure websites in both full and domain only modes.