EUREKA. I received the optical-powered splitter this afternoon (on a Sunday) and connected everything.
The TV remote turns on the TV, adjusts the TV speakers, and outputs to the optical port. The cable leads to the optical splitter.
One optical line from the splitter goes to the soundbar. The soundbar is turned on/off and the volume is with the soundbar controller.
The second optical line goes to the Phonak base station. Sound is adjusted via + and - switches on the side. The Roger On sits on the charging connection in the base and must be turned on. It recognizes the optical signal.
Now I have simultaneous sound from the TV speakers, the soundbar, and my hearing aids. Not as convenient as using HDMI ARC out, but well worth the trade-off.
A $20 product works and a $450 device does not.
My thanks to all of you who offered me suggestions.
Dennis