From the description of the service I did not guess that it was related to anything for which I'm using my machine. And I was mistaken in my previous post: I actually did NOT disable that Service on my other machine, which is why the PIN-login always worked there. I disabled it, but it is required for PIN-login. I discovered the solution in my case: it was related to the CNG Key Isolation Service (KeyIso). I liked the ability to sign-in with a PIN. Otherwise, let me know of any other way I might fix this. I don't think that could be related to this issue, but let me know if there is a Windows Service on which the 'Sign-in Options' depends. The last changes I had made to the OS were disabling some non-essential Services. Running sfc /scannow showed no integrity violations found. And if I logout, the login screen is still without 'Sign-in options' under my name.
However, it appears the PIN is immediately forgotten by Windows because even after I've finished, it still shows only 'Add' under the PIN section of Accounts -> Sign-in options. If I click on 'Add', I am allowed to add a PIN after entering my password. Under Settings, Accounts -> Sign-in options, I now see the option to 'Add' a PIN, as if I had never set a PIN. Now it has reverted to signing in with a password without the option to change back to PIN.
The 'Sign-in Options' link is suddenly missing from my Windows 10 login screen.