Password App not automatically popping up

When passwords were a part of the Settings, when a website or an app asked for a username/password, an autofill line would appear on the keyboard.

The new app does not do that. I have to start the password app and copy and paste items one by one (and every time I switch, it has to unlock).

On some sites that it works, it is erratic: one out of 4-5 times it functions right.

This is getting pretty frustrating. Is there a way to fix it or do we have to wait for the next releases of iOS and iPasOS?