Apparently, this approach does not work anymore, as I am getting "Cannot reset the password for accounts that uses Unity ID. Please try resetting your password in https://id.unity.com"
And in the "Edit account" settings it shows "Your account is configured to use your Unity ID to authenticate. If you'd like to change your password, you need to edit your Unity ID profile."
Does it mean that it's not possible anymore to switch to login/password authentication?