Update: Tested it further.
Secure Data Input works in Edge and Firefox.
Secure Data Input does not work in Chrome or when I enable containers for Firefox.
So the issue is the containers and strict site isolation. It seems Kaspersky is unable to inject their code to protect the password fields which is actually good news. If my AV can't inject code there, then malware can't either. But I contacted Kaspersky technical support to confirm for sure that it's due to App Containers.