PROGRESS (at least a bit...)
While browsing through another forum I think I may have discovered something relevant. I had suspected, based on others posts here and other places, that it was not the Samsung push services that broke this, but rather the Google Play Services.
The version of Google Play Services that my S6 was running was 7.0.99 but just today there was an update to version 7.3.29
I think that this is being rolled out slowly but if you go to
https://forums.androidcentral.com/e...d=com.google.android.gms&hl=en&token=rMWsNYq6 you can download and install.
What did this do? It did NOT restore the "from any screen" option so no, this is not a full fix. But what it DID do was to make the "OK Google" come up automatically on the home screen in TouchWiz, with Samsung Push still fully active and updated.
More importantly (perhaps?) is that also allowed the "OK Google" to come up in EVERY SCREEN of the Nova Launcher - even the APP DRAWER now responds to OK Google in Nova Launcher. It did none of those things before I updated Play Services.
So I wonder if Google is on the right track?