Well, clearing the phone (GS6) cache only worked for a short while, then the previous OK Google disconnect symptoms reappeared. Note that the watch retains its Bluetooth connection to the phone, and other watch-phone communications continue to work. A few hours after this, without me changing anything, I got a message saying that Android Wear on the watch had stopped, causing me to do a restart of the watch. I'm beginning to think something bad is going wrong.
So this morning, I did a factory reset of the phone. I hadn't done this before, but it is only a minor hassle. Took about a half hour. All my apps were reloaded on the phone, and my watch faces. However, my watch faces wouldn't communicate with the phone, though there were no errors. I did a resync of all apps - still didn't work. I tried OK Google. It accepted my "set a reminder" but then gave me the error about Google Play services not being on the phone. I seem to remember all this happening when I first got the watch. I had to do some other stuff fir an hour or so, then everything seemed to have sorted itself out somehow and for now everything is working again. I'll see how it goes for a day or so.
Google and/or Motorola (Lenova) need to sort out the watch reset stuff! It's very frustrating!
PS Somewhere in the above (I think after the Google Play services error) I did a clear cache on the phone again.